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Solve by the method of variation of parameters y" + 4y′ + 4y = 4 + e^-2x/x.

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Solve by the method of variation of parameters y" + 4y′ + 4y = 4 + e-2x/x.

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We have (D2 + 4D + 4) y = 4 + e-2x/x

A.E. is m2 + 4m + 4 = 0 

i.e., (m + 2)2 = 0 

m = – 2, – 2 

C.F. is yc = e–2x (C1 + C2x)

y = C1e–2x + C2xe–2x 

∴ y = Ae–2x + Bxe–2x ...(1)

be the complete solution of the given equation where A and B are to be found

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