MHT CET202020 Oct 2020Morning ShiftMathematicsDifferential EquationsActual
The solution of the differential equation ⁻¹ ( dy d x )=x+ y is
Options
- Ax= (x+y) (x+y)+c
- Bx= (x+y)- (x+y)+c
- Cx= (x+y)+ (x+y)+c
- Dx= x y+c
Correct answer
B. x= (x+y)- (x+y)+c
Step-by-step solution
We have ⁻¹ ( d y d x )=x+y dy dx = ( x + y ) Put x+y=t y=t-x d y d x = d t d x -1 dt dx =1+ t dt 1+ t = dx (1- t) (1+ t)(1- t) d t= d x x= 1- t 1- ² t d tx= 1- t ² t d t= ( ² t- t t ) d tx= t- t+cx= (x+y)- (x+y)+c