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Question

The degree of the differential equation $y left parenthesis x right parenthesis equals 1 plus fraction numerator d y over denominator d x end fraction plus fraction numerator 1 over denominator 1.2 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 2 end exponent plus fraction numerator 1 over denominator 1.2.3 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 3 end exponent plus$ is

2
3
1
4

hint Hint:

We are given a differential equation. We have to find the degree of the given differential equation.

The correct answer is: 1

The given differential equation is as follows:
$y left parenthesis x right parenthesis space equals 1 space plus fraction numerator d y over denominator d x end fraction plus fraction numerator 1 over denominator 1.2 end fraction open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared plus fraction numerator 1 over denominator 1.2.3 end fraction open parentheses fraction numerator d y over denominator d x end fraction close parentheses cubed$
We have to find the degree of differential equation.
Degree of a differential equation is power of the highest derivative in the given equation.
For this question, the highest derivative is $fraction numerator d y over denominator d x end fraction$
The highest power of this derivative is 3.
So, the power of the given differential equation is 3.

For such questions, we should know the definition of power.

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