# Quick question for Finding EOM with diff eq

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In summary, the conversation discusses a problem with finding the equation for x when given the equation of motion a = -bv, and using the method of separable equations. The individual was able to integrate the acceleration to find the velocity, but had trouble integrating to find x. They were unsure if they missed a step or if their answer was incorrect. The correct answer is x = x0 + (v0/b)(1-e-bt), which was found by taking the derivative of the book's answer.
I have been going through my old books again, and found myself a little stuck. I am not entirely sure if this would be better in this one or diffy eq.
The problem starts with having you find equation of motions when a= -bv, where b is constant and v = v(t)

Using method of separable equations, I was able to integrate the acceleration to get the velocity, v = v0e-bt

The problem is when I try to find the equation for x.
When I integrate v, using u substitution, I get x = (v0/b)e-bt+x0
The books says the answer x = x0 + (v0/b)(1-e-bt)
Also when I take the derivative of the book's answer, I get what I found for v

Am I way off base? Did I miss a step?

I get ##x = (v_{0}/b)e^{-bt}+x_{0}##

because this is wrong ... , the integral ##x=\int_{0}^{t}v_{0}e^{-bt}dt+x_{0}\not=\frac{v_{0}}{b}e^{-bt}+x_{0}##
control the signs! (and also the definite integral ...)
Ssnow

## 1. What is EOM and how is it related to differential equations?

EOM stands for "equation of motion" and is a mathematical representation of the motion of a physical system. It is often derived using differential equations, which describe how a system changes over time.

## 2. How do you find the EOM using differential equations?

To find the EOM using differential equations, you need to first identify the variables and parameters of the system, and then set up a differential equation that relates these variables. This equation can then be solved to find the EOM.

## 3. What are the applications of finding EOM with differential equations?

Finding EOM with differential equations has many applications in physics and engineering. It can be used to model the motion of objects, predict the behavior of systems, and design control systems for various applications.

## 4. Can EOM be found using other methods besides differential equations?

Yes, EOM can also be found using other methods such as Lagrangian mechanics or Hamiltonian mechanics. These methods may be more suitable for certain types of systems and can provide different insights into the behavior of the system.

## 5. Are there any software or tools available to help with finding EOM with differential equations?

Yes, there are many software and tools available that can assist with finding EOM with differential equations. Some popular options include MATLAB, Wolfram Mathematica, and Maple. These tools can also help with solving and visualizing the EOM once it has been derived.

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