(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the origin (0,0) is a critical point. Write the linear differential equation in operator format and solve.

2. Relevant equations

x'' + 10x' + 25x = 0

3. The attempt at a solution

I am not sure how to show that the origin is a critical point (without using a graph).

As for solving the 2nd-order linear differential equation, here's what I did:

x'' + 10x' + 25x = 0

Auxillary equation: m^{2}+ 10m + 25 = 0

Roots: m_{1}= m_{2}= -5

General solution: x = c_{1}e^{-5x}+ c_{2}xe^{-5x}

I believe my general solution is correct, but am not sure if I solved it by "operator method".

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Show that the origin is a critical point (linear differential equation)

**Physics Forums | Science Articles, Homework Help, Discussion**