What is the solution for y^{''}+36y=-36sec(6t) ?

The solution for y^{''}+36y=-36sec(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-ln(cos(6t))cos(6t)-6tsin(6t)

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y^{''}+36y=-36sec(6t)

y^{^{''}} + 36 y = - 36 sec (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) - ln (cos (6 t)) cos (6 t) - 6 t sin (6 t)

Solution steps

y^{''} (t) + 36 y = - 36 sec (6 t)

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - ln (cos (6 t)) cos (6 t) - 6 t sin (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) - ln (cos (6 t)) cos (6 t) - 6 t sin (6 t)

\frac{d}{d x} (e^{x} + 1)

(arctan (x))^{2}

\frac{\partial}{\partial x} (x^{6})

\int y e^{- \frac{y}{x}} d y

\int_{- \infty}^{0} \frac{1}{6 - 2 x} d x

What is the solution for y^{''}+36y=-36sec(6t) ?
The solution for y^{''}+36y=-36sec(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-ln(cos(6t))cos(6t)-6tsin(6t)