What is the solution for (d^2)/(dt^2)(θ(t))+4θ(t)=csc(2)(2t) ?

The solution for (d^2)/(dt^2)(θ(t))+4θ(t)=csc(2)(2t) is θ(t)=c_{1}cos(2t)+c_{2}sin(2t)+(csc(2)t)/2

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(d^2)/(dt^2)(θ(t))+4θ(t)=csc(2)(2t)

\frac{d ^{2}}{d t ^{2}} (θ (t)) + 4 θ (t) = csc (2) (2 t)

θ (t) = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{csc ( 2 ) t}{2}

Solution steps

\frac{d ^{2}}{d t ^{2}} (θ (t)) + 4 θ (t) = csc (2) (2 t)

Solve linear ODE:

θ (t) = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{csc ( 2 ) t}{2}

θ (t) = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{csc ( 2 ) t}{2}

y^{^{''}} - y^{^{'}} - 2 y = \frac{1}{5}

y^{^{''}} - 9 y = 5 e^{3 x}

y^{^{'''}} + 9 y^{^{''}} + 27 y^{^{'}} + 27 y = 3 e^{- 3 x}

y^{^{''}} + 16 y = 6 sin (4 x)

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

What is the solution for (d^2)/(dt^2)(θ(t))+4θ(t)=csc(2)(2t) ?
The solution for (d^2)/(dt^2)(θ(t))+4θ(t)=csc(2)(2t) is θ(t)=c_{1}cos(2t)+c_{2}sin(2t)+(csc(2)t)/2