What is the solution for y^{''}+ky=0 ?

The solution for y^{''}+ky=0 is y=c_{1}cos(sqrt(k)t)+c_{2}sin(sqrt(k)t)

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y^{''}+ky=0

y^{^{''}} + k y = 0

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

Solution steps

y^{''} (t) + k y (t) = 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)

x^{^{''}} - a x = 0

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = e^{3 x} cos (2 x)

y^{^{''''}} + 12 y^{^{''}} + 36 y = 0

2 \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

20 y^{^{''}} - 11 y^{^{'}} - 3 y = 0

What is the solution for y^{''}+ky=0 ?
The solution for y^{''}+ky=0 is y=c_{1}cos(sqrt(k)t)+c_{2}sin(sqrt(k)t)