What is the solution for y^{''}+64y=0,y(0)=0,y^'(0)=8 ?

The solution for y^{''}+64y=0,y(0)=0,y^'(0)=8 is y=sin(8t)

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y^{''}+64y=0,y(0)=0,y^'(0)=8

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = 8

y = sin (8 t)

Solution steps

y^{''} (t) + 64 y = 0

Solve linear ODE:

y = sin (8 t)

y = sin (8 t)

0.5 \frac{d ^{2} y}{d x ^{2}} + 2 y = 0

12 y^{^{''}} - 12 y^{^{'}} + 150 y = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 28

1124 y^{^{''}} + 5802 y^{^{'}} + 58292 y = 0

What is the solution for y^{''}+64y=0,y(0)=0,y^'(0)=8 ?
The solution for y^{''}+64y=0,y(0)=0,y^'(0)=8 is y=sin(8t)