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

The solution for y^{''}+36y=36sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-3tcos(6t)

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

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

y = c_{1} cos (6 t) + c_{2} sin (6 t) - 3 t cos (6 t)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - 3 t cos (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) - 3 t cos (6 t)

f (x) = x^{4} - 10 x^{2} + 9

\frac{d}{d x} (\frac{6}{x ^{2} + 36})

\int sin^{3} (x) cos^{3} (x) d x

(- 6, - 20), (1, 8)

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