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AP EAMCET2009MathematicsDifferential Equations

The solution of the differential equation d y d x = (x+y) (x+y)-1 is

Options

  1. Acosec (x+y)+ (x+y)=x+c
  2. Bx+ cosec (x+y)=c
  3. Cx+ (x+y)=c
  4. Dx+ (x+y)=c

Correct answer

B. x+ cosec (x+y)=c

Step-by-step solution

Given, d y d x = (x+y) (x+y)-1 aligned & Put x+y=z 1+ d y d x = d z d x & d z d x -1= z z-1 & z ^2 z d z= d x aligned aligned & Put z=t & z d z=d t & 1 t^2 d t=x-c - 1 t =x-c & - cosec z=x-c & x+ cosec (x+y)=c & aligned

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