Diff eq problem

  • Thread starter bmace
  • Start date
  • #1
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Homework Statement


Find x=x(t) given x(0) = -V0

(V0 + (a - b)t)(dx/dt) = (V0 + (a - b)t)a(2f-1) -bx

a and b are lambda in and lambda out


The Attempt at a Solution



Honestly don't know where to start that's why I came and asked it here .
The only thing I can think of is to make some kind of substitution somewhere.
 

Answers and Replies

  • #2
dextercioby
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Who's f ? Is it a constant, just like a, b, V_0 ? Do you know any method to integrate a first order ODE ?
 
  • #3
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yeah f is another constant, I've taken diff eq before, this is for a mathematical physics class, I just can't seem to get it down to a recognizable form that I know how to differentiate
 
  • #4
dextercioby
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Hmm, do you know the method of the integrating factor ? If so, then first, do some relabeling of functions and constants.

[tex] V_0 + (a-b) t =: f(t) [/tex]

[tex] a(2f-1) =: C [/tex]

Now your ODE looks like (assuming [itex] f(t)\neq 0 [/itex])

[tex] \frac{dx(t)}{dt} + \frac{b}{f(t)} x(t) = C [/tex]

Can you find the integrating factor ?
 
  • #5
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the integrating factor should be e^[tex]\int b/f(t)[/tex] = f(t)^b/f'(t)
 
  • #6
dextercioby
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Yes, but, please, pay attention to the notation used (missing paranthesis).

[tex] IF = f(t)^{\frac{b}{f'(t)}} = f(t)^{\frac{b}{a-b}} [/tex]
 
  • #7
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alright think I've got it Cf(t)^1/f'(t) + Kf(t)^(-b/f'(t))
where K is the constant of integration and from there just gotta plug in the intial conditions and solve for K
 
  • #9
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thanks really appreciate the help
 

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