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

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

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

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

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

Solution steps

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

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^{^{''}} - 2 y^{^{'}} - 3 y = 3 x e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} = x

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

y^{^{''}} - 12 y^{^{'}} + 36 y = 18 e^{6 x}

y^{^{''}} - 5 y^{^{'}} - 6 y = e^{x}

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