# Solve differential equation y'-2y= 1-2x

Solve differential equation${y}^{\prime }-2y=1-2x$
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

Szeteib

$dy/dx+p\left(x\right)y=Q\left(x\right)$
$I.F.={e}^{\int p\left(x\right)dx}$
$y\left(I.F.\right)=\int \left(I.F.\right)Q\left(x\right)+C$
$dy/dx-2y=\left(1-2x\right)$
p(x)= -2, Q(x)= (1-2x)
$I.F.={e}^{\int p\left(x\right)dx}$
$={e}^{\int -2dx}$
$y{e}^{-2x}=\int {e}^{2x}\left(1-2x\right)dx+c$
$y{e}^{-2x}=\left(1-2x\right){e}^{-2x}/-2-\left(-2\right){e}^{-2x}/4+c$ (${:}^{\prime }$ using by parts)
$y{e}^{-2x}=\left(\left(2x-1\right)/2\right){e}^{-2x}+{e}^{-2x}/2+C$
$y=\left(\left(2x-1\right)/2\right)+1/2+c{e}^{2x}$

###### Not exactly what you’re looking for?
Jeffrey Jordon

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee