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Math Help - differential equation

  1. #1
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    differential equation

    y'=x^2y+y cos x
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by kl.twilleger View Post
    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}
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