What is the solution for (D^2-2D)y=e^xsin(x) ?

The solution for (D^2-2D)y=e^xsin(x) is y=c_{1}e^{2x}+c_{2}-1/2 e^xsin(x)

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(D^2-2D)y=e^xsin(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 81 y = 9, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 21 y = e^{7 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y = - 48 e^{3 x}

\frac{1}{6} y^{^{''}} + 6 y = 4 tan (6 t) - \frac{1}{2} e^{t}

y^{^{''''}} + 2 y^{^{''}} + y = 3 + cos (2 x)

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