MHT CET202617 April 2026Evening ShiftMathematicsDifferential EquationsActual
The general solution of the differential equation y + (x - e^ y ) dy dx = 0 is...
Options
- Ae^ y = x + c
- Bxe^ y = e^ 2 y 2 + c
- C2x y = e^x + c
- Dy - e^ y = c
Correct answer
B. xe^ y = e^ 2 y 2 + c
Step-by-step solution
The given differential equation is y + (x - e^ y ) dy dx = 0 Rearranging the terms, we get: y dx dy + x - e^ y = 0 dx dy + x y = e^ y y This is a linear differential equation of the form dx dy + P(y)x = Q(y) , where P(y) = y and Q(y) = e^ y y . The integrating factor (IF) is: IF = e^ y dy = e^ y Multiplying the equation by the integrating factor and integrating, the solution is given by: x IF = Q(y) IF dy + c x e^ y = e^ y y e^ y dy + c x e^ y = e^ 2 y y dy + c Let y = t , then y dy = dt . The integral becomes: e^