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    Maths-
    General
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    Question

    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

    1. y equals x log invisible function application x plus x plus 2    
    2. y equals x log invisible function application x minus x plus 2    
    3. y equals x log invisible function application x plus x    
    4. y equals x log invisible function application x minus x    

    The correct answer is: y equals x log invisible function application x minus x plus 2

      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 Þ 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 fraction numerator 1 over denominator x end fractionÞ fraction numerator d y over denominator d x end fraction equals log invisible function application x plus c subscript 1 end subscript
      Þ y equals x log invisible function application x minus x plus c subscript 1 end subscript x plus c subscript 2 end subscript (on integrating twice)
      Given y equals 1and fraction numerator d y over denominator d x end fraction equals 0at x equals 1Þ c subscript 1 end subscript equals 0and c subscript 2 end subscript equals 2
      Therefore, the required solution is y equals x log invisible function application x minus x plus 2.

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