What is the solution for y^{''}+16y=3e^{3t} ?

The solution for y^{''}+16y=3e^{3t} is y=c_{1}cos(4t)+c_{2}sin(4t)+3/25 e^{3t}

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y^{''}+16y=3e^{3t}

y^{^{''}} + 16 y = 3 e^{3 t}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{3}{25} e^{3 t}

Solution steps

y^{''} (t) + 16 y = 3 e^{3 t}

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{3}{25} e^{3 t}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{3}{25} e^{3 t}

y^{^{''}} - y^{^{'}} + 2 y = cos (x), y (0) = 1, y^{^{'}} (0) = 0

y^{^{'''}} + 7 y^{^{''}} - 6 y^{^{'}} - 72 y = - 360

y^{^{''}} + 4 y^{^{'}} = 6 e^{3 t} - 3 e^{- t}

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

y^{^{''}} - 3 y^{^{'}} - 10 y = 54 e^{7 t}, y (0) = 5

What is the solution for y^{''}+16y=3e^{3t} ?
The solution for y^{''}+16y=3e^{3t} is y=c_{1}cos(4t)+c_{2}sin(4t)+3/25 e^{3t}