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