What is the solution for y^{''}+9y=30sin(t) ?

The solution for y^{''}+9y=30sin(t) is y=c_{1}cos(3t)+c_{2}sin(3t)+15/4 sin(t)

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y^{''}+9y=30sin(t)

y^{^{''}} + 9 y = 30 sin (t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{15}{4} sin (t)

Solution steps

y^{''} (t) + 9 y = 30 sin (t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{15}{4} sin (t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{15}{4} sin (t)

f (x) = e^{x} x

y = 8 cos (3 x), y = 8 sin (3 x), (0, \frac{π}{12})

f (x) = \frac{5}{x}, (1, 5)

\frac{d}{d x} ((x^{2} + x^{3})^{4})

\frac{\partial}{\partial x} (x \cdot y^{2} \cdot e^{z})

What is the solution for y^{''}+9y=30sin(t) ?
The solution for y^{''}+9y=30sin(t) is y=c_{1}cos(3t)+c_{2}sin(3t)+15/4 sin(t)