What is the solution for x^{''}+64x=0,x^'=0,x(0)=0.5 ?

The solution for x^{''}+64x=0,x^'=0,x(0)=0.5 is x=0.5cos(8t)

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x^{''}+64x=0,x^'=0,x(0)=0.5

x^{^{''}} + 64 x = 0, x^{^{'}} (0) = 0, x (0) = 0.5

x = 0.5 cos (8 t)

Solution steps

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

Solve linear ODE:

x = 0.5 cos (8 t)

x = 0.5 cos (8 t)

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = - 2, y^{^{'}} (0) = 9

x^{^{''}} + 0.5 \cdot x^{^{'}} + \frac{17}{16} \cdot x = 0

3 x^{^{''}} + 2 x^{^{'}} + 3 x = 0

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

What is the solution for x^{''}+64x=0,x^'=0,x(0)=0.5 ?
The solution for x^{''}+64x=0,x^'=0,x(0)=0.5 is x=0.5cos(8t)