What is the solution for (D^2+1)y=sec^3(x) ?

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

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(D^2+1)y=sec^3(x)

(D^{2} + 1) y = sec^{3} (x)

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

Solution steps

(D^{2} + 1) 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}

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