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Differential equation

  • #1
281
0
Can anyone help me solve

[tex]\dot{x} = Hx_0 \left( \sqrt{B} \frac{x_0}{x} + \sqrt{1-A-B} \right)[/tex]
 

Answers and Replies

  • #2
mjsd
Homework Helper
726
3
Can anyone help me solve

[tex]\dot{x} = Hx_0 \left( \sqrt{B} \frac{x_0}{x} + \sqrt{1-A-B} \right)[/tex]
what is what? in any case, try integrating factor method
 
  • #3
281
0
It's equivalent to solving

[tex]y \frac{dy}{dx} + ay + b = 0[/tex]
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,810
934
We need more information. Are you saying that A, B, H, and x0 are constants? Is so, simplify by letting
[tex]U= \frac{H\sqrt{B}x_0^2}{x}[/tex]
and
[tex]V= Hx_0\sqrt{1- A- B}[/itex]

So your equation becomes
[tex]\frac{dx}{dt}= \frac{U}{x}+ V= \frac{U+ Vx}{x}[/tex]
[tex]\frac{xdx}{U+ Vx}= dt[/itex]

That's easy to integrate.
 
Last edited by a moderator:
  • #5
281
0
Then I get

[tex]t= \frac{x}{V} -\frac{U}{V^2}ln(Vx+U)[/tex]

and trying to solve this for x is rather difficult?
 

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