What is the solution for y^{''}+36y=-36sec^2(6x) ?

The solution for y^{''}+36y=-36sec^2(6x) is y=c_{1}cos(6x)+c_{2}sin(6x)+1-ln(sec(6x)+tan(6x))sin(6x)

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y^{''}+36y=-36sec^2(6x)

y^{^{''}} + 36 y = - 36 sec^{2} (6 x)

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

Solution steps

y^{''} (x) + 36 y = - 36 sec^{2} (6 x)

Solve linear ODE:

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

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

f (x) = x + 6

x = 7 y, \frac{1}{3} y = x, \frac{1}{7} y = x

\frac{d}{d x} (ln (1 + sin^{2} (x)))

x \to - 7 lim (\frac{x ^{2} - 8}{7 - x})

\frac{d}{d x} (- cos (x) sin (x))

What is the solution for y^{''}+36y=-36sec^2(6x) ?
The solution for y^{''}+36y=-36sec^2(6x) is y=c_{1}cos(6x)+c_{2}sin(6x)+1-ln(sec(6x)+tan(6x))sin(6x)