What is the solution for y^{''}+4y=8e^{2t} ?

The solution for y^{''}+4y=8e^{2t} is y=c_{1}cos(2t)+c_{2}sin(2t)+e^{2t}

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y^{''}+4y=8e^{2t}

y^{^{''}} + 4 y = 8 e^{2 t}

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

Solution steps

y^{''} (t) + 4 y = 8 e^{2 t}

Solve linear ODE:

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

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

What is the solution for y^{''}+4y=8e^{2t} ?
The solution for y^{''}+4y=8e^{2t} is y=c_{1}cos(2t)+c_{2}sin(2t)+e^{2t}