# Solve differential equation dy/dx-(cot x)y= sin^3x

Solve differential equation $dy/dx-\left(cotx\right)y=si{n}^{3}x$
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SchepperJ

$dy/dx+Py=Q$
$P=-\mathrm{cot}x$, $Q={\mathrm{sin}}^{3}x$
$I.F.={e}^{\left(\int Pdx\right)}$
$={e}^{\left(\int -\mathrm{cot}xdx\right)}$

$y{e}^{\left(\int Pdx\right)}=\int Q{e}^{\left(\int Pdx\right)dx}+C$

(${:}^{\prime }\mathrm{cos}2x=1-2{\mathrm{sin}}^{2}x$)

$y=1/2x\mathrm{sin}x-1/4\mathrm{sin}x\mathrm{sin}2x+C$

Jeffrey Jordon