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)

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

y^{^{''}} - y^{^{'}} = 9 t e^{2 t}

q^{^{''}} + 20 q^{^{'}} + 100 q = 24, q (0) = 0, q^{^{'}} (0) = 0

(D^{2} + 1) y = e^{i x}

y^{^{''}} - 2 y^{^{'}} - 3 y = t^{2} + 3 e^{- t} cos (4 t)

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)