What is the solution for (D-1)^2y=(e^{2x}+sin(2x)) ?

The solution for (D-1)^2y=(e^{2x}+sin(2x)) is y=c_{1}e^x+c_{2}xe^x+e^{2x}-3/25 sin(2x)+4/25 cos(2x)

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(D-1)^2y=(e^{2x}+sin(2x))

(D - 1)^{2} y = (e^{2 x} + sin (2 x))

y = c_{1} e^{x} + c_{2} x e^{x} + e^{2 x} - \frac{3}{25} sin (2 x) + \frac{4}{25} cos (2 x)

Solution steps

(D - 1)^{2} y = e^{2 x} + sin (2 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + e^{2 x} - \frac{3}{25} sin (2 x) + \frac{4}{25} cos (2 x)

y = c_{1} e^{x} + c_{2} x e^{x} + e^{2 x} - \frac{3}{25} sin (2 x) + \frac{4}{25} cos (2 x)

What is the solution for (D-1)^2y=(e^{2x}+sin(2x)) ?
The solution for (D-1)^2y=(e^{2x}+sin(2x)) is y=c_{1}e^x+c_{2}xe^x+e^{2x}-3/25 sin(2x)+4/25 cos(2x)