1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simple ODE problem, Bernoulli's Equation

  1. Sep 5, 2011 #1
    [SOLVED] simple ODE problem, Bernoulli's Equation

    1. The problem statement, all variables and given/known data

    Initial value problem:

    Relation: t*y' - 2*[t^2]*sqrt(y) = 4*y
    Initial value: y(1) = 4

    2. Relevant equations

    general form of Bernoulli's equation:
    y' + a(t)y = b(t)*[y^n]

    First order, linear ODE form:
    y' + a(t)y = b(t)

    3. The attempt at a solution

    My written solution. I first get Bernoulli-type equation into first order/linear form. After that I solve it with the equation y = [1/mu]*Integral[ b(t) * mu dt] (+ constant)
    where mu = e^[ Integral[ a(t) dt]


    I have tried this multiple times and I get the same answer. When I plug in the solution y = f(t) it does not match the differential equation, (takes some time to show.)

    Any help would be great, I obviously am doing something wrong.
    Last edited: Sep 6, 2011
  2. jcsd
  3. Sep 5, 2011 #2
    Well it turns out I forgot how to multiply both sides of an equation.
    3rd to last step I multiply half of the right side by t^2, I'm not sure how to make this thread "solved."
  4. Sep 5, 2011 #3


    User Avatar
    Homework Helper

    I believe you can edit the header of your own posts, so you can put a " [SOLVED] " at the end of your title.
  5. Sep 6, 2011 #4
    k thanks ill do that
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook