Question: Help me this is a practice problem for my finals. I need to pass. With explanation pls! Thank you 1] Given f(D)y = x exsin3x

Help me this is a practice problem for my finals. I need to pass. With explanation pls! Thank you

1] Given f(D)y = x exsin3x + x2 . The roots of the auxiliary equation of yp assuming yp is the particular solution of some homogeneous linear differential equation with constant coefficients are : (a) 2 + 31,0 (b) 2 + 3i, 2 + 3i, 0,0 (c ) 2 + 31, 2 + 3i, 0,0,0 (d) 2 1 3i, 2 + 3i, 2 + 3i , 0,0 2] The linear differential -quation with constant coefficients satisfied by the equation y = 2x - 5e2x cos5x is (a) (D3 + 402 + 29D ) y=0 (b) (D4 - 4D3 + 29D2)y =0 (c) (D4 + 4D3 + 29D2)y = 0 (d) (D3 - 4D2 + 29D y =0

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