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

The solution for y^{''}+cy=0,y(0)=a,y^'(0)=0 is y=acos(sqrt(c)t)

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y^{''}+cy=0,y(0)=a,y^'(0)=0

y^{^{''}} + cy = 0, y (0) = a, y^{^{'}} (0) = 0

y = a cos (c t)

Solution steps

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

Solve linear ODE:

y = a cos (c t)

y = a cos (c t)

y^{^{''}} - 3 y^{^{'}} + (2.25 + a) y = 0, y (0) = 0

y^{^{''}} - 18 y^{^{'}} + 81 y = 0, y (0) = 0, y^{^{'}} (0) = 6

2 y^{^{''}} + 1000 y^{^{'}} + 2000000 y = 0

y^{^{''}} + a y = 0, y (0) = b, y^{^{'}} (0) = 0

9 y^{^{''}} - 8 y = 0

What is the solution for y^{''}+cy=0,y(0)=a,y^'(0)=0 ?
The solution for y^{''}+cy=0,y(0)=a,y^'(0)=0 is y=acos(sqrt(c)t)