Maths-

General

Easy

Question

The solution of the differential equation $x space d y divided by d x equals y left parenthesis log invisible function application y minus log invisible function application x plus 1 right parenthesis space$ is

$y = x e^{c x}$
$y + x e^{c x} = 0$
$y + e^{x} = 0$
None of these

hint Hint:

This is a homogenous equation.

The correct answer is: $y equals x e to the power of c x end exponent$

$x fraction numerator d y over denominator d x end fraction space equals space y open parentheses log y space minus space log x space plus space 1 close parentheses fraction numerator d y over denominator d x end fraction space equals space y over x open parentheses log y space minus space log x space plus space 1 close parentheses fraction numerator d y over denominator d x end fraction space equals space y over x open parentheses log y over x space plus space 1 close parentheses space space space space space space space space space space space space......... open parentheses 1 close parentheses L e t space y over x space equals space v therefore space y space equals space v x space space space space space space space space space space space space......... open parentheses 2 close parentheses D i f f e r e n t i a t i n g space b o t h space t h e space s i d e s comma fraction numerator d y over denominator d x end fraction space equals space v space plus space x fraction numerator d v over denominator d x end fraction space space space space space space space space space....... open parentheses 3 close parentheses P u t t i n g space e q n space open parentheses 2 close parentheses space a n d space open parentheses 3 close parentheses space i n space e q n space open parentheses 1 close parentheses comma space w e space g e t v space plus space x fraction numerator d v over denominator d x end fraction space equals space v open parentheses log v space plus space 1 close parentheses v space plus space x fraction numerator d v over denominator d x end fraction space equals space v log v space plus space v space x fraction numerator d v over denominator d x end fraction space equals space v log v fraction numerator d v over denominator v log v end fraction space equals space fraction numerator d x over denominator x end fraction I n t e g r a t i n g space b o t h space t h e space s i d e s comma integral fraction numerator d v over denominator v log v end fraction space equals space integral fraction numerator d x over denominator x end fraction integral fraction numerator 1 over denominator log v end fraction cross times 1 over v d v space equals space integral fraction numerator d x over denominator x end fraction space space space space space space space........ open parentheses 4 close parentheses L e t space log v space equals space t space space space space space space space........ open parentheses 5 close parentheses D i f f e r e n t i a t i n g space b o t h space t h e space s i d e s comma 1 over v d v space equals space d t space space space space......... open parentheses 6 close parentheses S u b s t i t u t i n g space e q n space open parentheses 5 close parentheses space a n d space open parentheses 6 close parentheses space i n space e q n space open parentheses 4 close parentheses comma space w e space g e t integral 1 over t d t space equals space integral 1 over x d x log t space equals space log x space plus space log c S u b s t i t u t i n g space t h e space v a l u e space o f space t comma log open parentheses log v close parentheses space equals space log open parentheses c x close parentheses log v space equals space c x S u b s t i t u t i n g space t h e space v a l u e space o f space v comma log open parentheses y over x close parentheses space equals space c x y over x space equals space e to the power of c x end exponent therefore y space equals space x e to the power of c x end exponent$

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x)

The solution of the differential equation $square root of a plus x end root fraction numerator d y over denominator d x end fraction plus x y equals 0$ is

Maths-General

General

maths-

The solution of $fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals sec to the power of 2 end exponent invisible function application x plus x e to the power of x end exponent$ is

maths-General

General

maths-

The solution of the differential equation $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals 1$ , given that $y equals 1 comma fraction numerator d y over denominator d x end fraction equals 0$ when $x equals 1$ , is

maths-General

General

maths-

Solution of $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

maths-General

General

maths-

Integrating factor of $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 3 end exponent minus 3$ is

maths-General

General

maths-

Integrating factor of differential equation $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

maths-General

General

maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus y equals cos invisible function application x$ is

maths-General

General

maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent$ is

maths-General

General

maths-

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y minus x over denominator y plus x end fraction$ is

maths-General

General

maths-

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x over denominator 2 y minus x end fraction$ is

maths-General

General

maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction$ is

maths-General

General

maths-

The solution of the differential equation $x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x$ is

maths-General

General

maths-

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x minus y end fraction$ is

maths-General

General

maths-

The solution of $fraction numerator d y over denominator d x end fraction plus square root of open parentheses fraction numerator 1 minus y to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction close parentheses end root equals 0$ is

maths-General

General

maths-

Solution of $y d x minus x d y equals x to the power of 2 end exponent y d x$ is

maths-General

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

The solution of the differential equation is

None of these

This is a homogenous equation.

The correct answer is:

Related Questions to study

The solution of the differential equation is

The solution of the differential equation is

The solution of is

The solution of is

The solution of the differential equation , given that when , is

The solution of the differential equation , given that when , is

Solution of is

Solution of is

Integrating factor of is

Integrating factor of is

Integrating factor of differential equation is

Integrating factor of differential equation is

The solution of the differential equation is

The solution of the differential equation is

The solution of the differential equation is

The solution of the differential equation is

Solution of differential equation is

Solution of differential equation is

The solution of the equation is

The solution of the equation is

The solution of the differential equation is

The solution of the differential equation is

The solution of the differential equation is

The solution of the differential equation is

The solution of the equation is

The solution of the equation is

The solution of is

The solution of is

Solution of is

Solution of is

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

Courses

Quick Links

The solution of the differential equation $x space d y divided by d x equals y left parenthesis log invisible function application y minus log invisible function application x plus 1 right parenthesis space$ is

$y = x e^{c x}$
$y + x e^{c x} = 0$
$y + e^{x} = 0$
None of these

The correct answer is: $y equals x e to the power of c x end exponent$

The solution of the differential equation $square root of a plus x end root fraction numerator d y over denominator d x end fraction plus x y equals 0$ is

The solution of the differential equation $square root of a plus x end root fraction numerator d y over denominator d x end fraction plus x y equals 0$ is

The solution of $fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals sec to the power of 2 end exponent invisible function application x plus x e to the power of x end exponent$ is

The solution of $fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals sec to the power of 2 end exponent invisible function application x plus x e to the power of x end exponent$ is

The solution of the differential equation $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals 1$ , given that $y equals 1 comma fraction numerator d y over denominator d x end fraction equals 0$ when $x equals 1$ , is

The solution of the differential equation $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals 1$ , given that $y equals 1 comma fraction numerator d y over denominator d x end fraction equals 0$ when $x equals 1$ , is

Solution of $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

Solution of $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

Integrating factor of $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 3 end exponent minus 3$ is

Integrating factor of $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 3 end exponent minus 3$ is

Integrating factor of differential equation $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

Integrating factor of differential equation $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus y equals cos invisible function application x$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus y equals cos invisible function application x$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent$ is

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y minus x over denominator y plus x end fraction$ is

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y minus x over denominator y plus x end fraction$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x over denominator 2 y minus x end fraction$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x over denominator 2 y minus x end fraction$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction$ is

The solution of the differential equation $x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x$ is

The solution of the differential equation $x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x minus y end fraction$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x minus y end fraction$ is

The solution of $fraction numerator d y over denominator d x end fraction plus square root of open parentheses fraction numerator 1 minus y to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction close parentheses end root equals 0$ is

The solution of $fraction numerator d y over denominator d x end fraction plus square root of open parentheses fraction numerator 1 minus y to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction close parentheses end root equals 0$ is

Solution of $y d x minus x d y equals x to the power of 2 end exponent y d x$ is

Solution of $y d x minus x d y equals x to the power of 2 end exponent y d x$ is