What is the solution for y^{''}+9y=-24sin(3t) ?

The solution for y^{''}+9y=-24sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+4tcos(3t)

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y^{''}+9y=-24sin(3t)

y^{^{''}} + 9 y = - 24 sin (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + 4 t cos (3 t)

Solution steps

y^{''} (t) + 9 y = - 24 sin (3 t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + 4 t cos (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + 4 t cos (3 t)

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

\int (x + 3) x + 3 d x

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 1

\frac{\partial}{\partial r} (r cos (s))

y = x, y = \frac{1}{2} x, x = 16

What is the solution for y^{''}+9y=-24sin(3t) ?
The solution for y^{''}+9y=-24sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+4tcos(3t)