NeoDevin
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Homework Statement
Use variation of parameters to find the general solution of:
x^2 y'' + xy' + 9y = -tan(3ln(x))
Homework Equations
y_p = y_2 (x) \int \frac{y_1 (x) g(x)}{W[y_1 (x),y_2 (x)]} dx - y_1 (x) \int \frac{y_2 (x) g(x)}{W[y_1 (x),y_2 (x)]} dx
The Attempt at a Solution
Solution for the homogeneous Euler equation is given by
<br /> y_1 (x) = cos(3ln(x)), y_2 (x) = sin(3ln(x))<br />
I try using these solutions in the equation for variation of parameters with:
W[y_1 , y_2] = \frac{3}{x}
g(x) = -tan(3ln(x))
The first term I can evaluate, but the second term gives me:
y_1 (x) \int \frac{x sin^2 (3ln(x))}{3 cos(3ln(x))} dx
which doesn't seem solvable by any methods I know...
Any suggestions on what to do from here, or where I went wrong on the way would be helpful.