What is the solution for y^{''}+9y=cos(3t),y(0)=1,y^'(0)=2 ?

The solution for y^{''}+9y=cos(3t),y(0)=1,y^'(0)=2 is y=cos(3t)+2/3 sin(3t)+(tsin(3t))/6

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y^{''}+9y=cos(3t),y(0)=1,y^'(0)=2

y^{^{''}} + 9 y = cos (3 t), y (0) = 1, y^{^{'}} (0) = 2

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}+9y=cos(3t),y(0)=1,y^'(0)=2 ?
The solution for y^{''}+9y=cos(3t),y(0)=1,y^'(0)=2 is y=cos(3t)+2/3 sin(3t)+(tsin(3t))/6