What is the solution for (d^2y)/(dx^2)+y=cot(x) ?

The solution for (d^2y)/(dx^2)+y=cot(x) is y=c_{1}cos(x)+c_{2}sin(x)+sin(x)ln(tan(x/2))

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(d^2y)/(dx^2)+y=cot(x)

\frac{d ^{2} y}{d x ^{2}} + y = cot (x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = cot (x)

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 5 e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- t}

x^{^{''}} + 5 x^{^{'}} + 4 x = 5 e^{10 t}

\frac{d ^{2} y}{d x ^{2}} + y = 1

3 y^{^{''}} + 8 y^{^{'}} + 4 y = e^{- 2 x}

What is the solution for (d^2y)/(dx^2)+y=cot(x) ?
The solution for (d^2y)/(dx^2)+y=cot(x) is y=c_{1}cos(x)+c_{2}sin(x)+sin(x)ln(tan(x/2))