What is the solution for (d^2y)/(dx^2)=-k^2y ?

The solution for (d^2y)/(dx^2)=-k^2y is y=c_{1}cos(kx)+c_{2}sin(kx)

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(d^2y)/(dx^2)=-k^2y

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

y = c_{1} cos (k x) + c_{2} sin (k x)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (k x) + c_{2} sin (k x)

y = c_{1} cos (k x) + c_{2} sin (k x)

x^{^{''}} + 144 x = 0, x (0) = 3, x^{^{'}} (0) = - 48

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = - 3

2 y^{^{''}} - 8 y^{^{'}} + 6 y = 0

y^{^{'''}} + 4 y^{^{''}} - 11 y^{^{'}} + 6 y = 0

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

What is the solution for (d^2y)/(dx^2)=-k^2y ?
The solution for (d^2y)/(dx^2)=-k^2y is y=c_{1}cos(kx)+c_{2}sin(kx)