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

The solution for y^{''}+9y=2sin(2t),y(0)=0,y^'(0)=-1 is y=-3/5 sin(3t)+2/5 sin(2t)

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y^{''}+9y=2sin(2t),y(0)=0,y^'(0)=-1

y^{^{''}} + 9 y = 2 sin (2 t), y (0) = 0, y^{^{'}} (0) = - 1

y = - \frac{3}{5} sin (3 t) + \frac{2}{5} sin (2 t)

Solution steps

y^{''} (t) + 9 y = 2 sin (2 t)

Solve linear ODE:

y = - \frac{3}{5} sin (3 t) + \frac{2}{5} sin (2 t)

y = - \frac{3}{5} sin (3 t) + \frac{2}{5} sin (2 t)

\frac{1}{1 - x - x ^{2}}, 0

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(ln (\frac{x}{3}))^{^{'}}

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What is the solution for y^{''}+9y=2sin(2t),y(0)=0,y^'(0)=-1 ?
The solution for y^{''}+9y=2sin(2t),y(0)=0,y^'(0)=-1 is y=-3/5 sin(3t)+2/5 sin(2t)