Manipal MET2016MathematicsDifferential Equations
The solution of the differential equation d y d x = (x+y) (x+y)-1 is
Options
- Acosec (x+y)+ (x+y)=x+C
- Bx+ cosec (x+y)=C
- Cx+ (x+y)=C
- 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