What is the solution for y^{''}+9y=2cos(3t) ?

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

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y^{''}+9y=2cos(3t)

y^{^{''}} + 9 y = 2 cos (3 t)

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

Solution steps

y^{''} (t) + 9 y = 2 cos (3 t)

Solve linear ODE:

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

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

x \to 0 lim (- \frac{2}{x})

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

\int_{0}^{1} (e^{x} + 1)^{2} d x

\int 3 - x x^{2} d x

\int \frac{( x ^{3} - 2 x )}{x} d x

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