What is the solution for y^{''}+4y=8sin(t) ?

The solution for y^{''}+4y=8sin(t) is y=c_{1}cos(2t)+c_{2}sin(2t)+8/3 sin(t)

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

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

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{8}{3} sin (t)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{8}{3} sin (t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{8}{3} sin (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 30 e^{2 x}

y^{^{''}} - 5 y^{^{'}} + 4 y = (12 x - 5) e^{4 x}

y^{^{''}} - 2 y^{^{'}} + y = sin (x)

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (x)

y^{^{''}} - y = tan (x)

What is the solution for y^{''}+4y=8sin(t) ?
The solution for y^{''}+4y=8sin(t) is y=c_{1}cos(2t)+c_{2}sin(2t)+8/3 sin(t)