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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

50 x^{^{''}} + 1 0^{6} x = 10

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 H (t)

y^{^{''}} + 9 y = 12 cos (3 t), y (0) = 0, y^{^{'}} (0) = 6

y^{^{''}} + 4 y^{^{'}} + 5 = 4 e^{- 2 t} tan (t)

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- x} (cos (x))

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