What is the solution for y^{''}+9y=3sec^3(3x) ?

The solution for y^{''}+9y=3sec^3(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+(tan(3x)sin(3x))/6

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y^{''}+9y=3sec^3(3x)

y^{^{''}} + 9 y = 3 sec^{3} (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{tan ( 3 x ) sin ( 3 x )}{6}

Solution steps

y^{''} (x) + 9 y = 3 sec^{3} (3 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{tan ( 3 x ) sin ( 3 x )}{6}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{tan ( 3 x ) sin ( 3 x )}{6}

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

y^{^{''}} + (- 3) y^{^{'}} + 4 y = 16 x - 12 e^{2 x}

y^{^{''''}} - 3 y^{^{'''}} + 2 y^{^{''}} = 4 x

y^{^{''}} + 6 y^{^{'}} + 8 y = 16 t^{2}

y^{^{''}} + 4 y = u_{π} (t)

What is the solution for y^{''}+9y=3sec^3(3x) ?
The solution for y^{''}+9y=3sec^3(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+(tan(3x)sin(3x))/6