What is the solution for y^{''}+0y+64y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+0y+64y=0,y(0)=1,y^'(0)=0 is y=cos(8t)

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y^{''}+0y+64y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 0 y + 64 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = cos (8 t)

Solution steps

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

Solve linear ODE:

y = cos (8 t)

y = cos (8 t)

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} = 0

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y^{^{'}} (0) = 2

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 5 y = 0

y^{^{'''}} + 3 y^{^{''}} - 18 y^{^{'}} - 40 y = 0

y^{^{''}} + 2 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 3

What is the solution for y^{''}+0y+64y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+0y+64y=0,y(0)=1,y^'(0)=0 is y=cos(8t)