Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Equation

  1. Sep 1, 2008 #1
    I'm wondering if you could find a solution to the following differential equation


    where L(t)=∫l(t)dt
    β is a constant

    I've been tryint to find a solution for ages. Please help!
  2. jcsd
  3. Sep 1, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Economist2008! Welcome to PF! :smile:

    Your equation is very confusing.

    Can you tell us what the context is?

    If dw/dL(t) = β is constant, then w = βL. :confused:
  4. Sep 1, 2008 #3
    Re: Welcome to PF!

    Thanks for replying Tim,

    Ok let me tell you the whole story of my problem. The variable I would like to solve for is ψ(t), which is a co-state variable for the state variable L(t). ψ(t) has the meaning of what an additional increment of labour supply is worth for the future, because wage goes up with L(t).

    The context is that I want to find the optimal time to get children. l(t) is the instantaneous labour supply of some female at time t. L(t) is the cumulative amount of labor up to time t. The wage w(L(t)) depends positively on the cumulative labour supply. L(t) can be thought of being a measure for experience. Wage goes up the more working experience the female has.

    If you know the answer, I would be very happy and could continue with the paper. Thanks. :-)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook