What is the solution for y^{''}+16y=56cos(4t) ?

The solution for y^{''}+16y=56cos(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)+7tsin(4t)

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y^{''}+16y=56cos(4t)

y^{^{''}} + 16 y = 56 cos (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + 7 t sin (4 t)

Solution steps

y^{''} (t) + 16 y = 56 cos (4 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + 7 t sin (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + 7 t sin (4 t)

x^{^{''}} + 5 x^{^{'}} + 17 x = 12 cos (3 t)

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} (2 x + 5)

y^{^{''}} + y = 3 sin (2 t), y (0) = 12, y^{^{'}} (0) = 1

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

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 e^{4 x}

What is the solution for y^{''}+16y=56cos(4t) ?
The solution for y^{''}+16y=56cos(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)+7tsin(4t)