dy/dx +2y/x = 4x
find general solution
dy/dx= 4x + x/2y
2y dy = 4x + x dx
2y dy = 5x dx
integrate
y^2 = 2.5 x^2 + C
What you have done is not correct.
Your DE is not separable, you need to use the integrating factor method.
Do you know this method?
Read this http://www.mathhelpforum.com/math-he...equations.html
Yep, great work, now multipling $\displaystyle x^2$ through the whole equation you get
$\displaystyle x^2 \times (y' + \frac{2}{x} ~y = 4x) = y'x^2+2xy= 4x^3$
and
$\displaystyle y'x^2+2xy= 4x^3$
by the product rule
$\displaystyle x^2y= \int 4x^3~dx$
Now can you take it from here?