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)

y^{^{'''}} + 25 y^{^{'}} = 10 sin (5 t) - 4 t^{2}

y^{^{''}} + y = 1, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + y = 4000 sec (40 x)

a x^{^{''}} + b x^{^{'}} + c = 0

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 10 y = 4 e^{5 t}

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)