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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + 2 y = \frac{e ^{x}}{cos ( x )}

y^{^{'''}} + 9 y^{^{'}} = - 18 t

y^{^{''}} + 16 y = 5 sec (4 x)

y^{^{'''}} + 4 y^{^{'}} = cos (x)

y^{^{''}} + y = sin (x) - cos (x)

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