MHT CET202615 April 2026Morning ShiftMathematicsDifferential EquationsActual
The solution of the differential equation dy dx = e^ x-y + x^2 e^ -y is...
Options
- Ay = e^x + c
- Be^y = e^x + x^3 + c
- Ce^y = e^x + x^3 3 + c
- De^y = e^x + 2x + c
Correct answer
C. e^y = e^x + x^3 3 + c
Step-by-step solution
The given differential equation is dy dx = e^ x-y + x^2 e^ -y This can be rewritten by factoring out e^ -y as dy dx = e^ -y (e^x + x^2) Separating the variables, we get e^y dy = (e^x + x^2) dx Integrating both sides, we get e^y dy = (e^x + x^2) dx e^y = e^x + x^3 3 + c Answer: e^y = e^x + x^3 3 + c