differential equation

Quote:

Originally Posted by kl.twilleger

$y'=x^2y+y cos x$

$\begin{aligned}\frac{dy}{dx}&=x^2y+y\cos(x)=y(x^2+ \cos(x))\\<br /> &\implies\frac{dy}{y}=\bigg[x^2+\cos(x)\bigg]dx\\<br /> &\implies\int\frac{dy}{y}=\ln|y|=\int\bigg[x^2+\cos(x)\bigg]dx=\frac{x^3}{3}+\sin(x)+C\\<br /> &\implies{y=\pm{C_1e^{\frac{x^3}{3}+\sin(x)}}}<br /> \end{aligned}$