What is the solution for y^{''}+9y=18sin(3t) ?

The solution for y^{''}+9y=18sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-3tcos(3t)

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y^{''}+9y=18sin(3t)

y^{^{''}} + 9 y = 18 sin (3 t)

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

Solution steps

y^{''} (t) + 9 y = 18 sin (3 t)

Solve linear ODE:

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

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

x \to 0 + lim (sin (x^{x}))

\frac{( 1 - ln ( x ) )}{11 x ^{2}}

\int_{- 1}^{3} ∣ x ∣ d x

\int \frac{6 x + 6}{x ^{2} + 2 x - 3} d x

\int 2 x y cos (x y^{2}) d y

What is the solution for y^{''}+9y=18sin(3t) ?
The solution for y^{''}+9y=18sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-3tcos(3t)