What is the solution for y^{''}+36y=-60sin(6t) ?

The solution for y^{''}+36y=-60sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)+5tcos(6t)

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y^{''}+36y=-60sin(6t)

y^{^{''}} + 36 y = - 60 sin (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) + 5 t cos (6 t)

Solution steps

y^{''} (t) + 36 y = - 60 sin (6 t)

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + 5 t cos (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) + 5 t cos (6 t)

\frac{d y}{d t} = - 2 (1 + y^{2}) tan (2 t)

\frac{d}{d x} (\frac{( x - 7 )}{x + 7})

\int e^{2 x} sin (3 x) d x

\int_{1}^{12} \frac{1}{x - 9} d x

n = 1 \sum \infty \frac{1}{n + 4}

What is the solution for y^{''}+36y=-60sin(6t) ?
The solution for y^{''}+36y=-60sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)+5tcos(6t)