What is the solution for y^{''}+9y=2sin(2t) ?

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

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y^{''}+9y=2sin(2t)

y^{^{''}} + 9 y = 2 sin (2 t)

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

Solution steps

y^{''} (t) + 9 y = 2 sin (2 t)

Solve linear ODE:

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

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

x^{2}, x, 0, 1

\frac{d y}{d x} = y (550 - y)

\int \frac{1}{sin ^{2} ( a ) x} + c d x

\int \frac{25 x ^{2} - 16}{x ^{4}} d x

y = \frac{2}{3 x ^{4}}

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