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

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

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

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

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

Solution steps

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

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)

2 y^{^{''}} + 5 y^{^{'}} + 2 y = 0

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

(d^{5} + 8 d^{3} + 16 d) y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y (1) = 0

\frac{d ^{2} x}{d t ^{2}} + 81 x = 0

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