What is the solution for (d^2y)/(dx^2)+ky=0 ?

The solution for (d^2y)/(dx^2)+ky=0 is y=c_{1}cos(sqrt(k)x)+c_{2}sin(sqrt(k)x)

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(d^2y)/(dx^2)+ky=0

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

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

Solution steps

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

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)

(D^{2} + 4)^{2} y = 0

y^{^{'''}} + 6 y^{^{''}} - 245 y^{^{'}} - 64 y = 0

- a^{2} y^{^{''}} = k y

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

y^{^{''}} - 20 y^{^{'}} + 116 y = 0

What is the solution for (d^2y)/(dx^2)+ky=0 ?
The solution for (d^2y)/(dx^2)+ky=0 is y=c_{1}cos(sqrt(k)x)+c_{2}sin(sqrt(k)x)