What is the solution for y^{''}+c^2y=0,y(0)=a,y^'(0)=0 ?

The solution for y^{''}+c^2y=0,y(0)=a,y^'(0)=0 is y=acos(ct)

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y^{''}+c^2y=0,y(0)=a,y^'(0)=0

y^{^{''}} + c^{2} y = 0, y (0) = a, y^{^{'}} (0) = 0

y = a cos (c t)

Solution steps

y^{''} (t) + c^{2} y = 0

Solve linear ODE:

y = a cos (c t)

y = a cos (c t)

x^{^{''}} + 10 x^{^{'}} + 29 x = 0, x^{^{'}} (0) = 6

y^{^{''}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 10, y^{^{'}} (0) = - 9

y^{^{''}} - 4 y^{^{'}} - 4 y = 0, y (0) = 1, y^{^{'}} (0) = 5

What is the solution for y^{''}+c^2y=0,y(0)=a,y^'(0)=0 ?
The solution for y^{''}+c^2y=0,y(0)=a,y^'(0)=0 is y=acos(ct)