Solve by undermined coefficients/variation of parameters: \[ y''-4y'+4y = \frac{e^{2x}}{x}\]

Solve by undermined coefficients/variation of parameters: \[ y''-4y'+4y = \frac{e^{2x}}{x}\]

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\[ y_c''-4y_c'+4y_c=0\]\[ \lambda^2-4\lambda+4=0\]\[ \lambda=2, 2\]\[y_c = c_1e^{2x}+c_2xe^{2x}\] How can I guess the particular solution?

you can't do this one with undetermined cofficients. you would have to use variation of parameter.

to find the yp

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