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#### karush

##### Well-known member

- Jan 31, 2012

- 2,929

\textit{Find } \mu(x): &\mu(x) =\exp\left(\int \dfrac{1}{x}\,dx\right)=e^{\ln{x}}=x\\

\textit{multiply thru by x} &xy^\prime+y=3x\cos 2x\\

\textit{rewrite as } &(xy)'=3x\cos 2x \\

\textit{}integrate &xy=\int 3x\cos 2x \, dx=\dfrac{3}{2}x\sin(2x)+\dfrac{3}{4}\cos(2x)+c\\

\textit{divide thru by x} &y=\dfrac{3}{2}\sin(2x)+\dfrac{3}{4}\dfrac{\cos(2x)}{x}+\dfrac{c}{x}\\

\textit{re-order} &y=\dfrac{c}{x}+\dfrac{3}{4}\dfrac{\cos 2x}{x}+\dfrac{3}{2}\sin 2x

\end{array}$

ok quite sure there are some oops in this one

thot I would try array to do the steps so....

hopefully there kinda

Mahalo for input

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