What is the solution for y^{''}+9y+y=0,y(0)=0.16,y^'(0)=0 ?

The solution for y^{''}+9y+y=0,y(0)=0.16,y^'(0)=0 is y=0.16cos(sqrt(10)t)

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y^{''}+9y+y=0,y(0)=0.16,y^'(0)=0

y^{^{''}} + 9 y + y = 0, y (0) = 0.16, y^{^{'}} (0) = 0

y = 0.16 cos (10 t)

Solution steps

y^{''} (t) + 9 y + y = 0

Solve linear ODE:

y = 0.16 cos (10 t)

y = 0.16 cos (10 t)

y^{^{''}} - 7 y^{^{'}} - 2 y = 0

2 y^{^{''}} + 14 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

4 y^{^{''}} + 7 y^{^{'}} + 3 y = 0

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (- 1) = 5, y^{^{'}} (- 1) = 2

c y^{^{''}} + ab y^{^{'}} = 0, y (0) = 1, y (1.2) = 0

What is the solution for y^{''}+9y+y=0,y(0)=0.16,y^'(0)=0 ?
The solution for y^{''}+9y+y=0,y(0)=0.16,y^'(0)=0 is y=0.16cos(sqrt(10)t)