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MHT CET202122 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

The general solution of ⁻¹ ( d y d x )=x+y is

Options

  1. A(x+y)- (x+y)=x^2+c
  2. B(x+y)+ (x+y)=x^2+c
  3. C(x+y)+ (x+y)=x+c
  4. D(x+y)- (x+y)=x+c

Correct answer

D. (x+y)- (x+y)=x+c

Step-by-step solution

aligned & ⁻¹ ( d y d x )=x+y & d y d x = (x+y) & Put x+y=t 1+ d y d x = d t d x & d t d x -1= t d t d x =1+ t & d t 1+ t = d x & (1- t) d t 1- t= d x 1- t ^2 t d t= d x & ( ^2 t- sect t ) d t= d x & t- t=x+c & (x+y)- (x+y)=x+c aligned

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