What is the solution for (D^2-4D+4)y=sin(3x) ?

The solution for (D^2-4D+4)y=sin(3x) is y=c_{1}e^{2x}+c_{2}xe^{2x}-5/169 sin(3x)+12/169 cos(3x)

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(D^2-4D+4)y=sin(3x)

(D^{2} - 4 D + 4) y = sin (3 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{5}{169} sin (3 x) + \frac{12}{169} cos (3 x)

Solution steps

(D^{2} - 4 D + 4) y = sin (3 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{5}{169} sin (3 x) + \frac{12}{169} cos (3 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{5}{169} sin (3 x) + \frac{12}{169} cos (3 x)

y^{^{''}} - 2 y^{^{'}} - 15 = 0, y (0) = 2, y^{^{'}} (0) = 6

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{3 x} - x^{2}

\frac{d ^{2} y}{d x ^{2}} + 4 y = - 3 x^{2} + 2 x + 3

y^{^{''}} + 16 y = g (t), y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 t} ln (t)

What is the solution for (D^2-4D+4)y=sin(3x) ?
The solution for (D^2-4D+4)y=sin(3x) is y=c_{1}e^{2x}+c_{2}xe^{2x}-5/169 sin(3x)+12/169 cos(3x)