# Solve differential equation xy'+3y=x^2

Question
Solve differential equation $$xy'+3y=x^2$$

2021-02-04
$$dy/dx+(3y)/x=x$$
$$I.F.= e^(int 3/x dx)= e^(3lnx)$$
$$I.F.= x^3$$
$$yx^3= int x^3(x^2)dx+c$$
$$yx^3= int x^5 dx+c$$
$$yx^3= x^6/+c$$
$$y= x^3/6+cx^(-3)$$

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