What is the solution for y^{''}+9y=9sec(3t) ?

The solution for y^{''}+9y=9sec(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+ln(cos(3t))cos(3t)+3tsin(3t)

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y^{''}+9y=9sec(3t)

y^{^{''}} + 9 y = 9 sec (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + ln (cos (3 t)) cos (3 t) + 3 t sin (3 t)

Solution steps

y^{''} (t) + 9 y = 9 sec (3 t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + ln (cos (3 t)) cos (3 t) + 3 t sin (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + ln (cos (3 t)) cos (3 t) + 3 t sin (3 t)

y^{^{''}} - y^{^{'}} + 81 y = 9 sin (9 t)

y^{^{''}} + 4 y = 16 t, y^{0} = 3, y^{^{'}} 0 = - 6

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

y^{^{''}} - 7 y = t^{2}

(y^{^{''}} + 2 y^{^{'}} + 5) = e^{x}

What is the solution for y^{''}+9y=9sec(3t) ?
The solution for y^{''}+9y=9sec(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+ln(cos(3t))cos(3t)+3tsin(3t)