The general solution of differential equation $\frac{d y}{d x}=e^{x+y}+x^2 e^{x^3+y}$ is (where $\mathrm{C}$ is a constant of integration.)

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Aicharya · Accepted Answer

$\begin{aligned} & \frac{d y}{d x}=e^{x+y}+x^2 e^{x^3+y} \ & \Rightarrow \frac{d y}{d x}=e^y\left(e^x+x^2 e^{x^3}ight) \ & \Rightarrow \int e^{-y} d y=\int\left(e^x+x^2 e^{x^3}ight) d x \ & \Rightarrow-e^{-y}+c=e^x+\frac{1}{3} e^{x^3} \ & \Rightarrow e^x+e^{-y}+\frac{1}{3} e^{x^3}=c\end{aligned}$

The general solution of differential equation $\frac{d y}{d x}=e^{x+y}+x^2 e^{x^3+y}$ is (where $\mathrm{C}$…

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