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

Solve differential equation${y}^{\prime }+3y=3{x}^{2}{e}^{\left(}-3x\right)$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

hajavaF

${y}^{\prime }+3y=3{x}^{2}{e}^{-3x}$
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
$y\left(I.F.\right)=\int \theta \left(I.F.\right)dx+C$
$y{e}^{3x}=\int 3{x}^{2}{e}^{-3x3x}edx+C$
$y{e}^{3x}=\int 3{x}^{2}dx+C$
$y{e}^{3x}=\left(3{x}^{3}\right)/3+C$
$y{e}^{3}x={x}^{3}+C$
$y={e}^{-3x}\left({x}^{3}+C\right)$

Jeffrey Jordon