# Math Help - calculus first order differential equation~

1. ## calculus first order differential equation~

could i get some help solving the DE's

y' = (-2/x)y + (x^2)(e^x)

thank you where y(1) = (sqrt(2))e

2. Originally Posted by pandakrap
could i get some help solving the DE's

y' = (-2/x)y + (x^2)(e^x)

thank you where y(1) = (sqrt(2))e

This can be solve using an integrating factor

$y'+\frac{2}{x}y=x^2e^{x}$

$I(x)=e^{\int \frac{2}{x}dx}=e^{\ln(x^2)}=x^2$

So if we multiply the equation by the integrating factor we get

$x^2y'+2xy=x^4e^{x} \iff \frac{d}{dx}\left( x^2y\right)=x^4e^{x}$

you now just need to integrate both sides and solve for y.

The right hand side will be integration by parts 4 times.

Good luck.

3. you are my life savor man, thanks so much