What is the solution for x^{''}+64x=0,x(0)= 4/12 ,x^'(0)=0 ?

The solution for x^{''}+64x=0,x(0)= 4/12 ,x^'(0)=0 is x= 1/3 cos(8t)

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x^{''}+64x=0,x(0)= 4/12 ,x^'(0)=0

x^{^{''}} + 64 x = 0, x (0) = \frac{4}{12}, x^{^{'}} (0) = 0

x = \frac{1}{3} cos (8 t)

Solution steps

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

Solve linear ODE:

x = \frac{1}{3} cos (8 t)

x = \frac{1}{3} cos (8 t)

y^{^{'''}} - 2 y^{^{''}} + 8 y^{^{'}} = 0

y^{^{''}} + 16 y = 0, y^{^{'}} (0) = 3, y (0) = 5

5 y^{^{''}} + 25 y = 0

y^{^{''}} - 15 y^{^{'}} + 54 y = 0, y (0) = 9, y^{^{'}} (0) = 6

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

What is the solution for x^{''}+64x=0,x(0)= 4/12 ,x^'(0)=0 ?
The solution for x^{''}+64x=0,x(0)= 4/12 ,x^'(0)=0 is x= 1/3 cos(8t)