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

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

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

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

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

Solution steps

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

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

y^{^{''}} + y = x e^{x}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + (- 4) y^{^{'}} + 3 y = - 12

7 y^{^{''}} - 20 y^{^{'}} + 12 y = 8 e^{2}

y^{^{''}} + y = 2 sin (t)

y^{^{''}} - 2 y^{^{'}} + 10 y = 18 e^{x} sec (3 x)

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