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

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

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

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

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

4 y^{^{''}} - y = e^{\frac{x}{2}} + 4

y^{^{''}} + 4 y = 3 csc (2 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- t}, y (0) = 2, y^{^{'}} (0) = 2

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{6 + e ^{x}}

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{5 + e ^{x}}

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