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Thread: differential equation

  1. November 13th 2008, 02:35 PM #1
    kl.twilleger
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    differential equation

    y'=x^2y+y cos x
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  2. November 13th 2008, 02:39 PM #2
    Mathstud28
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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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