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Solving Differential Equations by Variation of Parameters

Determine the particular solution of the following nonhomogeneous differential equation using the method of variation of parameters
y" + 4y' + 4y = x^-2 e^-2x ; x>0

homogeneous equation is y =C1e^-2x +C2xe^-2x

y= u1e^-2x +u2xe^-2x
after differentiating and letting u'1e^-2x +u'2xe^-2x =0,
we have _2u'e^-2x -2'u2xe^-2x = x^-2e^-2x
please take it from here!

Text gives answer of y = C1e^-2x + C2xe^-2x lnx

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