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

The solution for (d^2-3d+2)y=sin(2x) is y=c_{1}e^{2x}+c_{2}e^x-1/20 sin(2x)+3/20 cos(2x)

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(d^2-3d+2)y=sin(2x)

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

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} = 2 x^{2}

(d^{2} + 4 d + 4) y = 10 e^{- x} cos (x)

(d^{2} + 5 d + 6) \cdot y = e^{x} + e^{- x}

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = x^{2} + x

(d^{3} - 3 d + 2) \cdot y = x + 1

What is the solution for (d^2-3d+2)y=sin(2x) ?
The solution for (d^2-3d+2)y=sin(2x) is y=c_{1}e^{2x}+c_{2}e^x-1/20 sin(2x)+3/20 cos(2x)