What is the solution for y^{''}=2y+22cot^3(x),y(0)=11cot(x) ?

The solution for y^{''}=2y+22cot^3(x),y(0)=11cot(x) is

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y^{''}=2y+22cot^3(x),y(0)=11cot(x)

y^{^{''}} = 2 y + 22 cot^{3} (x), y (0) = 11 cot (x)

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{11 2 e ^{- 2 x} cot ^{3} ( x )}{2} d x + e^{- 2 x} \cdot \int - \frac{11 2 e ^{2 x} cot ^{3} ( x )}{2} d x

Solution steps

y^{''} (x) = 2 y + 22 cot^{3} (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{11 2 e ^{- 2 x} cot ^{3} ( x )}{2} d x + e^{- 2 x} \cdot \int - \frac{11 2 e ^{2 x} cot ^{3} ( x )}{2} d x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{11 2 e ^{- 2 x} cot ^{3} ( x )}{2} d x + e^{- 2 x} \cdot \int - \frac{11 2 e ^{2 x} cot ^{3} ( x )}{2} d x

2 y^{^{''}} + 18 y + 5 = 0, y (0) = 0, y^{^{'}} (0) = 0

y, (d^{3} + 4 d) y = 2 t + t^{2}

y^{^{''}} - 9 y = x

y^{^{''}} + y = 2 \cdot e^{x}

y^{^{''}} - y^{^{'}} - 6 y = 10 x e^{3 x} + 17 e^{3 x}

What is the solution for y^{''}=2y+22cot^3(x),y(0)=11cot(x) ?
The solution for y^{''}=2y+22cot^3(x),y(0)=11cot(x) is