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bron * +4y'+4y = 2 xe *** +8sin (2x) auxilliary equation is ma +4m+4 = 0 m=-2,-2 yo = (4 +c2x)e-2 The two linearly independent solutions of complementary solution are (x) = eº, y(x)= xerºx The nonhomogeneous part of de is 2xe*** +8 sin (2x) Derivatives of nonhomogeneous part of de are xe 2*, -2*, sin (2x), cos (2x) and are of the form xe-* for the non-negative integer k=1 so y(x)= Ax*e^2* + B sin (2x) +C cos(2x) P
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