Register to reply 
Superficially simple vector differential equation problem 
Share this thread: 
#1
Feb1813, 10:36 AM

P: 10

Hi,
I have the following vector differential equation (numerator layout derivatives): [tex]\frac{\partial e(v)}{\partial v}=\frac{1}{\beta} \frac{\partial w(v)}{\partial v} \Gamma^{1}[/tex] where both ##e(v)## and ##w(v)## are scalar functions of the vector ##v##, and where ##\Gamma## is a symmetric invertible matrix with all columns (and rows) summing to 1. The naive solution would be ##e(v)=\frac{1}{\beta} w(v) \Gamma^{1}##, but this is incorrect since ##e(v)## is a scalar. Clearly, when ##\Gamma## is the identity matrix, ##e(v)=\frac{1}{\beta} w(v)## is a valid solution. My question is, does a solution exist for any other value of ##\Gamma##? Tom 


Register to reply 
Related Discussions  
Simple Differential Equation (Ordinary Differential Equation)  Differential Equations  7  
Stuck in solving a (rather simple) differential equation problem.  Calculus & Beyond Homework  3  
Simple problem in Mechanics, weird differential equation  Introductory Physics Homework  4  
A simple differential equation problem.  Differential Equations  13  
Vector Differential Equation  Differential Equations  1 