What is the solution for y^{''}+4y=e-t ?

The solution for y^{''}+4y=e-t is y=c_{1}cos(2t)+c_{2}sin(2t)-t/4+e/4

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y^{''}+4y=e-t

y^{^{''}} + 4 y = e - t

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{t}{4} + \frac{e}{4}

Solution steps

y^{''} (t) + 4 y = e - t

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{t}{4} + \frac{e}{4}

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{t}{4} + \frac{e}{4}

What is the solution for y^{''}+4y=e-t ?
The solution for y^{''}+4y=e-t is y=c_{1}cos(2t)+c_{2}sin(2t)-t/4+e/4