What is the solution for y^{''}+64y=0,y(0)=0,y^'(0)= 64/5 ?

The solution for y^{''}+64y=0,y(0)=0,y^'(0)= 64/5 is y= 8/5 sin(8t)

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y^{''}+64y=0,y(0)=0,y^'(0)= 64/5

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{64}{5}

y = \frac{8}{5} sin (8 t)

Solution steps

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

Solve linear ODE:

y = \frac{8}{5} sin (8 t)

y = \frac{8}{5} sin (8 t)

y^{^{''''}} + 4 y^{^{'''}} + 4 y^{^{''}} = 0

4 y^{^{''}} + 4 y^{^{'}} + 325 y = 0, y (0) = 3, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = - 2, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 25 \cdot y = 0

x^{^{''}} = - x^{^{'}} + 3 x

What is the solution for y^{''}+64y=0,y(0)=0,y^'(0)= 64/5 ?
The solution for y^{''}+64y=0,y(0)=0,y^'(0)= 64/5 is y= 8/5 sin(8t)