Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm desperately trying to find the solution of this simple ODE: $$\frac{dx}{dt}= C +\frac{x-a_1}{b_1} + \frac{x-a_2}{b_2} $$

Where C is a constant. Someone has a clue?

Thanks for the feedback already: Ok some more info: I think I can solve this by substituting $x$ by $e^{t}$. In that case I get:

$$ e^t = C+\frac{e^t-a_1}{b_1} + \frac{e^t-a_2}{b_2}$$ But now I'm stuck. Does it mean x is just: $$ x (1-1/b_1 -1/b_2)= (C-a_1/b_a -a_2/b_2) $$ But then it is no longer depending on t... Iḿ doing something wrong here

share|improve this question
    
Welcome to math,SE. What do you find difficult in the question?? Have you tries separating the variables?? –  TheJoker Oct 13 '12 at 13:29

2 Answers 2

This is a time-invariant linear ODE with constant coefficients. The solution is therefore $x(t) = a+be^{\lambda t}$ for some $a,b,\lambda \in \mathbb{R}$. By substituting that for $x$ in your ODE and comparing the coefficients you can easily find the particular values of $a,b,\lambda$.

share|improve this answer

Hints:

  • Write the equation in the form: $x' + c_1 x = c_2$.
  • Use an integrating factor or notice that the equation is separable.

Don't forget to handle any special cases when calculating $c_1$ and $c_2$.

share|improve this answer
    
Ok, but what would be the solution to $x′+c_1x=c_2$? –  user44558 Oct 13 '12 at 14:19
    
@user44558 See here, particularly the first example. Which method(s) have you learned so far for solving linear first order differential equations? –  Ayman Hourieh Oct 13 '12 at 17:32

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.