What is the solution for (d^2y)/(dx^2)+y=(sec(x))^3 ?

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

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(d^2y)/(dx^2)+y=(sec(x))^3

\frac{d ^{2} y}{d x ^{2}} + y = (sec (x))^{3}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 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 = 2 e^{5 t}

4 y^{^{''}} + y = sin (2 x)

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

y^{^{''}} + y = cos (x - \frac{π}{2}), y (0) = 0, y^{^{'}} (0) = 0

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

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