# Solve differential equation y'+3y= 3x^2 e^(-3x)

OlmekinjP 2021-02-09 Answered
Solve differential equation${y}^{\prime }+3y=3{x}^{2}{e}^{\left(}-3x\right)$
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## Expert Answer

hajavaF
Answered 2021-02-10 Author has 90 answers

${y}^{\prime }+3y=3{x}^{2}{e}^{-3x}$
Compairing with genral form of a linear diffrential equation
${y}^{\prime }+Py=\theta$
with integrating factor $IF={e}^{\int Pdx}$
we have P = 3, $\theta =3{x}^{2}{e}^{-3x}$
$I.F.={e}^{\int 3dx}={e}^{3x}$
:. Its solution is given by
$y\left(I.F.\right)=\int \theta \left(I.F.\right)dx+C$
$y{e}^{3x}=\int 3{x}^{2}{e}^{-3x3x}edx+C$
$y{e}^{3x}=\int 3{x}^{2}dx+C$
$y{e}^{3x}=\left(3{x}^{3}\right)/3+C$
$y{e}^{3}x={x}^{3}+C$
$y={e}^{-3x}\left({x}^{3}+C\right)$

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Jeffrey Jordon
Answered 2021-12-14 Author has 2070 answers

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