MHT CET202619 April 2026Evening ShiftMathematicsDifferential EquationsActual
The solution of the differential equation dy dx = (x + y) is...
Options
- A( x + y 2 ) = x + c
- B( x + y 2 ) = x + c
- C- (x + y) = x + c
- D(x - y) + x = c
Correct answer
B. ( x + y 2 ) = x + c
Step-by-step solution
Let x + y = v Differentiating with respect to x , we get 1 + dy dx = dv dx dy dx = dv dx - 1 Substituting this in the given differential equation: dv dx - 1 = v dv dx = 1 + v dv 1 + v = dx Integrating both sides: dv 2 ^2 ( v 2 ) = dx 1 2 ^2 ( v 2 ) dv = dx ( v 2 ) = x + c Substituting v = x + y : ( x + y 2 ) = x + c