# Solve the differential equation (dP)/dt=4P+a

Solve the differential equation $\left(dP\right)/dt=4P+a$
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FieniChoonin

$\left(dP\right)/dt=4P+a$
$\left(dP\right)/dt-4P=a$
$I.F.={e}^{\int -4dt}={e}^{-4t}$
$p{e}^{-4t}=\int a{e}^{-4t}dt+c$
$p{e}^{-4t}=\left(a{e}^{-4t}\right)/-4+c$
$p=-a/4+c{e}^{-4t}$

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