Homogenous Ordinary Differential Equation

[sndoyle1]

Homework Statement

x²y"-(x²+2x)y'+(x+2)y=0

known solutions:

y₁(2)=2
y₁'(2)=1
y₂(2)=2e²
y₂'(2)=3e²

Determine the wronskian

Homework Equations

y_c=C1e^r1x+C2e^r2x

I also know how to find the wronskian via a determinant

The Attempt at a Solution

I have tried to divide out the first x² term to make this a linear system, not sure how to simplify after this to find the characteristic solution.

 

[sndoyle1]

I found the answer using Abel's theorem.

 

[sandy.bridge]

nvm: I see you found your answer.

Isn't the complementary general solution equations you provided for differential equations with constant coefficients, rather than coefficients that are functions of a variable?

 

[sndoyle1]

you are correct. I was confused with the question and obviously drew a blank.