Solve the following differential equation. dy/dx = e^(x+y) + x^2 e^y

Question

Solve the following differential equation.

\(\cfrac{dy}{dx} = e^{x+y}+x^2e^y\)

dy/dx = e^x+y + x² e^y

Answer 1

\(\cfrac{dy}{dx} = e^{x+y}+x^2e^y\)

Integrating both sides, we get

∴ 3e^x + 3e^-y + x³ = -3c₁

∴ 3e^x + 3e^-y + x³ = c, where c = -3c₁

This is the general solution.