The solution of the DE dy/dx = e^x+y + x^2 . e^y is

Question

The solution of the DE \(\frac{dy}{dx}\) = e^x+y + x² . e^y is

A. e^x-y + \(\frac{x^3}{3}\) + C

B. e^x + e^-y  + \(\frac{x^3}{3}\) + C'

C.  e^x - e^-y  + \(\frac{x^3}{3}\) + C

D. None of these

Answer 1

Given \(\frac{dy}{dx}\) = e^x+y + x² e^y 

On integrating on both sides, we get

Conclusion: Therefore, e^-y + e^x + \(\frac{x^3}{3}\) = C is the 

solution of \(\frac{dy}{dx}\) = e^x+y + x²e^y