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
$\displaystyle y'+\frac{2}{x}y=x^2e^{x}$
$\displaystyle I(x)=e^{\int \frac{2}{x}dx}=e^{\ln(x^2)}=x^2$
So if we multiply the equation by the integrating factor we get
$\displaystyle x^2y'+2xy=x^4e^{x} \iff \frac{d}{dx}\left( x^2y\right)=x^4e^{x}$
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.