What is the solution for y^{''}+36y=36sec^2(6t) ?

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

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y^{''}+36y=36sec^2(6t)

y^{^{''}} + 36 y = 36 sec^{2} (6 t)

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

Solution steps

y^{''} (t) + 36 y = 36 sec^{2} (6 t)

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} = - 4 - 6 x

y^{^{''}} + y^{^{'}} - 2 y = 1 + t, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + y = 2 tan (x)

\frac{1}{2} x^{^{''}} + \frac{1}{2} x^{^{'}} - 6 x = 10 cos (3 t)

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x + 5

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