MHB What Methods Solve This Initial Value ODE?

oasi
Messages
14
Reaction score
0
how can we solve this ODE?

http://img818.imageshack.us/img818/3966/59962234.png
 
Physics news on Phys.org
oasi said:
how can we solve this ODE?

http://img818.imageshack.us/img818/3966/59962234.png

Start by solving the homogeneous solution.
 

Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
View full post »

Similar threads

A Seeking advice about solving an ODE
  • · Replies 3 ·
Replies
3
Views
3K
I Non-linear ODE: initial conditions
  • · Replies 4 ·
Replies
4
Views
2K
I Can initial conditions for an ODE be given by functions instead of constants?
  • · Replies 10 ·
Replies
10
Views
2K
I 2nd order ODE numerical solution
  • · Replies 9 ·
Replies
9
Views
3K
A How to Find Initial Conditions for a Fifth Order ODE in Visco-Elastic Models?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Solving an Initial Value Problem Analytically
  • · Replies 5 ·
Replies
5
Views
2K
I When and How to Solve ODEs: Clarity for Confused Students
  • · Replies 3 ·
Replies
3
Views
2K
MHB Why ODE Linear? Initial Value Problem Explanation
  • · Replies 2 ·
Replies
2
Views
2K
I What is a symmetric ODE / what does it mean when an ODE is symmetric?
  • · Replies 1 ·
Replies
1
Views
2K
I Solving an ODE with Legendre Polynomials
  • · Replies 1 ·
Replies
1
Views
2K