What is the solution for y^{''}-3y^'+2y=e^tsin(t) ?

The solution for y^{''}-3y^'+2y=e^tsin(t) is y=c_{1}e^{2t}+c_{2}e^t+1/2 e^tcos(t)-1/2 e^tsin(t)

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y^{''}-3y^'+2y=e^tsin(t)

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{t} sin (t)

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

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = e^{t} sin (t)

Solve linear ODE:

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

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

What is the solution for y^{''}-3y^'+2y=e^tsin(t) ?
The solution for y^{''}-3y^'+2y=e^tsin(t) is y=c_{1}e^{2t}+c_{2}e^t+1/2 e^tcos(t)-1/2 e^tsin(t)