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Wellesley
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Homework Statement
Given that x, x2 and 1/x are solutions of the homogeneous equation corresponding to:
[tex]
x^3y''' + x^2y''-2xy'+2y=2x^4
[/tex]
x>0
determine a particular solution.
Homework Equations
The Attempt at a Solution
I'm trying to solve this problem using three simultaneous equations:
[tex]
u_1'x + u_2'x^2 + u_3'*(1/x) = 0
[/tex]
[tex]u_1' + 2u_2'x - u_3'x^{-2}= 0[/tex]
[tex]2u_2' + 2u_3'x^{-3}= 2x^4[/tex]
Then, when I try and solve for u1, u2 and u3, I seem to doing it incorrectly, the wrong answer. I've come back to this problem several times over the last three days, and all that has changed were the answers I'm getting! Should I be trying a different method in solving this problem?
Thanks.
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