What is the solution for y^{''}+9y=0,y(0)=0,y^'(0)=3 ?

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

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y^{''}+9y=0,y(0)=0,y^'(0)=3

y^{^{''}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 3

y = sin (3 t)

Solution steps

y^{''} (t) + 9 y = 0

Solve linear ODE:

y = sin (3 t)

y = sin (3 t)

y^{^{''}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 1

(d^{4} + 1) y = 0

y^{^{''''}} + 9 y^{^{''}} = 0

25 y^{^{''}} - 120 y^{^{'}} + 144 y = 0

y^{^{'''}} - 7 y^{^{''}} + 16 y^{^{'}} - 12 y = 0

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