What is the solution for y^{''}+9y=8sin(t),y(0)=0,y^'(0)=4 ?

The solution for y^{''}+9y=8sin(t),y(0)=0,y^'(0)=4 is y=sin(3t)+sin(t)

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y^{''}+9y=8sin(t),y(0)=0,y^'(0)=4

y^{^{''}} + 9 y = 8 sin (t), y (0) = 0, y^{^{'}} (0) = 4

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

Solution steps

y^{''} (t) + 9 y = 8 sin (t)

Solve linear ODE:

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

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = 10 e^{3 t}

y^{^{''}} - 6 y^{^{'}} + 3 y = x e^{x}

3 y^{^{''}} + 8 y^{^{'}} + 4 y = 8 x^{2} - 8 x + 2 + e^{- 2 x}

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

What is the solution for y^{''}+9y=8sin(t),y(0)=0,y^'(0)=4 ?
The solution for y^{''}+9y=8sin(t),y(0)=0,y^'(0)=4 is y=sin(3t)+sin(t)