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

The solution for (d^2y)/(dt^2)+k^2y=0 is y=c_{1}cos(kt)+c_{2}sin(kt)

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(d^2y)/(dt^2)+k^2y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

10 y^{^{''}} + 12 y^{^{'}} - 18 y = 0

y^{^{'''}} + 19 y^{^{''}} + 97 y^{^{'}} + 79 y = 0

y^{^{''}} + 3 y^{^{'}} - 16 y = 0

4 y^{^{''}} + 4 y^{^{'}} + 17 y = 0, y (0) = 2

x^{^{''}} + x^{^{'}} + \frac{1}{2} x = 0

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