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Manipal MET2016MathematicsDifferential 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

We have, d y d x = (x+y) (x+y)-1 (i) Put x+y=v , we get 1+ d y d x = d v d x Put x+y=v , we get 1+ d y d x = d v d x d y d x = d v d x -1 Eq. (i) reducing to d v d x = v v d v v v =d x cosec v v d v= d x array ll & - cosec v v=x+C & - cosec (x+y)=x+C & x+ cosec (x+y)=C array

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