(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".

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

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