Solving Linear Systems Using Variation of Parameters

[ravager1987]

Homework Statement

(x²+1)y"+(2-x²)-(2+x)y=x(x+1)²

given 2 associated homogeneous solution are: e^x and 1/x

Homework Equations

this is a question from shaum's outline differential equations chapter on "variation of parameters"

The Attempt at a Solution

so here what i got...
y_h=C₁e^x+C₂(1/x)

and now I am trying to find particular solution of y:

v₁'e^x+v₂'(1/x)=0
and

v₁'e^x+v₂'(-1/x²)=x(x+1)²/(x²+1)and now I am stucked at solving v₁' and v₂' someone help please?

 

[foxjwill]

Well, you have a system of two linear equations, right? What methods do you know to solve those?