What is the solution for y^{''}+9y=12sin(3t) ?

The solution for y^{''}+9y=12sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-2tcos(3t)

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y^{''}+9y=12sin(3t)

y^{^{''}} + 9 y = 12 sin (3 t)

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

Solution steps

y^{''} (t) + 9 y = 12 sin (3 t)

Solve linear ODE:

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

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

x \to 2 lim (\frac{x ^{3}}{3} - 7 x^{2})

f (y) = y^{4}

\frac{d ^{2}}{d x ^{2}} (sec (\frac{π}{4}))

\int sec (x) tan (x) - 9 e^{x} d x

\int_{1}^{3} x^{2} e^{x} d x

What is the solution for y^{''}+9y=12sin(3t) ?
The solution for y^{''}+9y=12sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-2tcos(3t)