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

The solution for y^{''}+9y=cos(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+(tsin(3t))/6

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

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

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{t sin ( 3 t )}{6}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{t sin ( 3 t )}{6}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{t sin ( 3 t )}{6}

\int x^{2} \cdot 1 + x d x

\frac{\partial}{\partial x} (- e^{8 y} cos (8 x) \cdot 8)

d er i v a t i v e y = tan (π x)

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

x \to - 2 lim (6 - 3 x - 3)

What is the solution for y^{''}+9y=cos(3t) ?
The solution for y^{''}+9y=cos(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+(tsin(3t))/6