What is the solution for x^{''}+ax=0 ?

The solution for x^{''}+ax=0 is x=c_{1}cos(sqrt(a)t)+c_{2}sin(sqrt(a)t)

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x^{''}+ax=0

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

x = c_{1} cos (a t) + c_{2} sin (a t)

Solution steps

x^{''} (t) + a x (t) = 0

Solve linear ODE:

x = c_{1} cos (a t) + c_{2} sin (a t)

x = c_{1} cos (a t) + c_{2} sin (a t)

y^{^{''}} + 3 y^{^{'}} + 5 y = 0

y^{^{''''}} - 10 y^{^{'''}} + 25 y^{^{''}} = 0

y^{^{''}} + 9 y^{^{'}} + 20 y = 0

(4 D^{5} - 23 D^{3} - 33 D^{2} - 17 D - 3) y = 0

\frac{d ^{2} x}{d t ^{2}} + 5 \frac{d x}{d t} + 4 x = 0

What is the solution for x^{''}+ax=0 ?
The solution for x^{''}+ax=0 is x=c_{1}cos(sqrt(a)t)+c_{2}sin(sqrt(a)t)