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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int_{0}^{c} 4 e^{2 x} d x

\int_{0}^{1} (e^{x} - x e^{x^{2}}) d x

\int \frac{v}{1 - v} d v

\int - x + 3 (cos (\frac{n \cdot π \cdot x}{8})) d x

\frac{d}{d x} (\frac{1}{x y})

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