What is the solution for y^{''}+9y=30sin(3t) ?

The solution for y^{''}+9y=30sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-5tcos(3t)

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y^{''}+9y=30sin(3t)

y^{^{''}} + 9 y = 30 sin (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) - 5 t cos (3 t)

Solution steps

y^{''} (t) + 9 y = 30 sin (3 t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) - 5 t cos (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) - 5 t cos (3 t)

2 \cdot x \cdot y^{2} + 2 \cdot x + (x^{2} \cdot y + 4 \cdot y) \cdot y^{^{'}} = 0

\frac{d}{d y} (x^{2} + x y)

7 x^{6} e^{x} + e^{x} x^{7}

\int cos (3 x + 5) d x

\frac{d}{d t} (2 t)

What is the solution for y^{''}+9y=30sin(3t) ?
The solution for y^{''}+9y=30sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-5tcos(3t)