What is the solution for y^{''}+16y=8sin(4t) ?

The solution for y^{''}+16y=8sin(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)-tcos(4t)

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y^{''}+16y=8sin(4t)

y^{^{''}} + 16 y = 8 sin (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) - t cos (4 t)

Solution steps

y^{''} (t) + 16 y = 8 sin (4 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) - t cos (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) - t cos (4 t)

y^{''} + y = 8 H (t - 5)

\frac{d ^{2} y}{d x ^{2}} + y = sin (2)

y^{^{''}} - y^{^{'}} - 6 y = 14 cos (3 x)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{4 x}

y^{^{'''}} + 7 y^{^{''}} - 8 y = x e^{x} + 12

What is the solution for y^{''}+16y=8sin(4t) ?
The solution for y^{''}+16y=8sin(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)-tcos(4t)