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

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

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y^{''}+y=sec^3(x)

y^{^{''}} + y = sec^{3} (x)

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

Solution steps

y^{''} (x) + y = sec^{3} (x)

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 9 e^{- 3 x}

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

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3} e^{2 t}

y^{^{''}} - 2 y^{^{'}} + y = x e^{x}

y^{^{''}} - 3 y^{^{'}} + 2 y = cos (x), y (0) = 0, y^{^{'}} (0) = 2

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