What is the solution for y^{''}+16y=csc^2(4t) ?

The solution for y^{''}+16y=csc^2(4t) is y=c_{1}cos(4t)+c_{2}sin(4t)+(-ln(tan(2t))cos(4t)-1)/(16)

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y^{''}+16y=csc^2(4t)

y^{^{''}} + 16 y = csc^{2} (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- ln ( tan ( 2 t ) ) cos ( 4 t ) - 1}{16}

Solution steps

y^{''} (t) + 16 y = csc^{2} (4 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- ln ( tan ( 2 t ) ) cos ( 4 t ) - 1}{16}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- ln ( tan ( 2 t ) ) cos ( 4 t ) - 1}{16}

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{- 3 x}

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

y^{^{''}} - y^{^{'}} - 2 y = 6 x + 5 e^{4 x}

y^{^{''}} - 4 y^{^{'}} - 12 y = e^{- 2 x} + 5 x + 2

y^{^{''}} - 4 y^{^{'}} + 5 y = 24 cos (x)

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