What is the solution for y^{''}+36y=12tan(6t) ?

The solution for y^{''}+36y=12tan(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-(cos(6t)ln(tan(6t)+sec(6t)))/3

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y^{''}+36y=12tan(6t)

y^{^{''}} + 36 y = 12 tan (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) )}{3}

Solution steps

y^{''} (t) + 36 y = 12 tan (6 t)

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) )}{3}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) )}{3}

What is the solution for y^{''}+36y=12tan(6t) ?
The solution for y^{''}+36y=12tan(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-(cos(6t)ln(tan(6t)+sec(6t)))/3