What is the solution for y^{''}+4y=9sin(t),y(0)=1,y^'(0)=-1 ?

The solution for y^{''}+4y=9sin(t),y(0)=1,y^'(0)=-1 is y=cos(2t)-2sin(2t)+3sin(t)

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y^{''}+4y=9sin(t),y(0)=1,y^'(0)=-1

y^{^{''}} + 4 y = 9 sin (t), y (0) = 1, y^{^{'}} (0) = - 1

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} = 2 e^{x}

9 y^{^{''}} - 16 y = sin (x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 cos^{2} (2 x)

y^{^{''}} + 25 y = 3, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 20 y^{^{'}} + 200 y = 400

What is the solution for y^{''}+4y=9sin(t),y(0)=1,y^'(0)=-1 ?
The solution for y^{''}+4y=9sin(t),y(0)=1,y^'(0)=-1 is y=cos(2t)-2sin(2t)+3sin(t)