# Solve differential equation y'+4y=128x

Solve differential equation${y}^{\prime }+4y=128x$
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d2saint0

${y}^{\prime }+4y=128x$
${y}^{\prime }+Py=Q$

$I.F.={e}^{\int Pdx}$
$={e}^{\int 4dx}$
$y\left(I.F.\right)=\int Q\left(I.F.\right)dx+c$
$y{e}^{4x}=\int 128x{e}^{4x}dx+c$
$y{e}^{4x}=128\int x{e}^{4x}dx+c$
$y{e}^{4x}=128\left[x\frac{{e}^{4x}}{4}-\int 1×\frac{{e}^{4x}}{4}dx\right]+c$
$y{e}^{4x}=128\left[\frac{x{e}^{4x}}{4}-\frac{1}{16}{e}^{4x}\right]+c$
$y\left(x\right)=32x-8+c{e}^{4x}$

Jeffrey Jordon