What is the solution for y^{''}+y= 1/((sin(x))^3) ?

The solution for y^{''}+y= 1/((sin(x))^3) is y=c_{1}cos(x)+c_{2}sin(x)+(-csc(x)+2cot(x)cos(x))/2

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y^{''}+y= 1/((sin(x))^3)

y^{^{''}} + y = \frac{1}{( sin ( x ) ) ^{3}}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{- csc ( x ) + 2 cot ( x ) cos ( x )}{2}

Solution steps

y^{''} (x) + y = \frac{1}{( sin ( x ) ) ^{3}}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{- csc ( x ) + 2 cot ( x ) cos ( x )}{2}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{- csc ( x ) + 2 cot ( x ) cos ( x )}{2}

(D^{2} - 4 D + 4) y = 8 e^{2 x} x^{2} sin (2 x)

x^{^{''}} - x = - 1

y^{^{''}} + 6 y^{^{'}} + 9 y = cos (3 x)

3 y^{^{''}} - 10 y^{^{'}} - 13 y = 13 x - 3

y^{^{''}} + 2 y^{^{'}} - 3 y = t e^{- 3 t}

What is the solution for y^{''}+y= 1/((sin(x))^3) ?
The solution for y^{''}+y= 1/((sin(x))^3) is y=c_{1}cos(x)+c_{2}sin(x)+(-csc(x)+2cot(x)cos(x))/2