CUET Preparation Today
The general solution of the differential equation \(\frac{dy}{dx}=e^{x-y}+x^2e^{-y}\) is |
\(e^y=e^x+\frac{x^3}{3}+c\) \(e^y=e^x+\frac{x^3}{3}\) \(y=x+e^{\frac{x^3}{3}}+c\) \(e^x=e^y+\frac{y^3}{3}+c\) |
\(e^y=e^x+\frac{x^3}{3}+c\) |
\(\frac{dy}{dx}=e^{-y}(e^x+x^2)\) so $\int e^ydy=\int e^x+x^2dx$ $⇒e^y=e^x+\frac{x^3}{3}+C$ |
