What is the solution for (d^2f)/(dx^2)+k^2f(x)=0 ?

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

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(d^2f)/(dx^2)+k^2f(x)=0

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

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

Solution steps

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

Solve linear ODE:

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

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

2 y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

x^{^{''}} + 8 x^{^{'}} = 0, x (0) = - 3, x^{^{'}} (0) = 5

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

y^{^{''}} - 14 y^{^{'}} + 113 y = 0

y^{^{''}} - 6 y^{^{'}} + 15 y = 0

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