What is the solution for y^{''}+9y=12cos(3t),y(0)=0,y^'(0)=6 ?

The solution for y^{''}+9y=12cos(3t),y(0)=0,y^'(0)=6 is y=2tsin(3t)+2sin(3t)

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

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

y = 2 t sin (3 t) + 2 sin (3 t)

Solution steps

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

Solve linear ODE:

y = 2 t sin (3 t) + 2 sin (3 t)

y = 2 t sin (3 t) + 2 sin (3 t)

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

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

y^{^{''}} - 2 y^{^{'}} = 3, y (0) = - 3 e^{- x}

y^{^{''}} + 9 y^{^{'}} + 18 y = x + e^{- x}

y^{^{''}} + 49 y = 4 t^{3} sin (7 t)

What is the solution for y^{''}+9y=12cos(3t),y(0)=0,y^'(0)=6 ?
The solution for y^{''}+9y=12cos(3t),y(0)=0,y^'(0)=6 is y=2tsin(3t)+2sin(3t)