What is the solution for y^{''}+5y=e^t ?

The solution for y^{''}+5y=e^t is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)+1/6 e^t

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y^{''}+5y=e^t

y^{^{''}} + 5 y = e^{t}

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{6} e^{t}

Solution steps

y^{''} (t) + 5 y = e^{t}

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{6} e^{t}

y = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{6} e^{t}

What is the solution for y^{''}+5y=e^t ?
The solution for y^{''}+5y=e^t is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)+1/6 e^t