How do you solve x''(t)+x3=0?

Get the solution to "How do you solve x''(t)+x3=0?"

Kali Thomas

2022-04-10

maggionmoo

Beginner2022-04-11Added 16 answers

x^{″} (t) + 3 x = 0

is a linear homogeneous second order ordinary differential equation.
Suppose we try the solution:

x = e^{p t}

Then:

x^{″} = p^{2} e^{p t}

(p^{2} + 3) e^{p t} = 0

p = \pm \sqrt{3} i

The linear combination of the individual solutions is also a solution. Hence the general solution is:

x = A e^{i \sqrt{3} t} + B e^{- i \sqrt{3} t}

where A and B are constants.
Since

e^{i θ} = \cos θ + i \sin θ

, we can re-arrange the above to

x = C \cos \sqrt{3} t + D \sin \sqrt{3} t

where C=A+B and D=A-B

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?