1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Separable Differential Equations

  1. Nov 3, 2008 #1
    1. The problem statement, all variables and given/known data

    I'm having trouble understanding my class notes from a lecture on separable differential equations.

    I would like to solve the equation g(y)y' = f(x)

    3. The attempt at a solution

    g(y)y' = f(x), G(x), F(x) exists and are continuous

    The left side is the derivative of G(y(x)) and the right is F(x) + C

    [tex]\frac{d}{dx} G(y(x)) = \frac{d}{dx} F(x) + C[/tex]

    G'(y(x))y'(x) = g(y(x))y'(x)

    [tex]\frac{d}{dx} (F(x) + C) = F'(x) + 0 = f(x)[/tex]

    G(y(x)) = F(x) + C

    So do you simply do

    G-1(G(y(x))) = y(x) = G-1(F(x)) + G-1(C) ?
  2. jcsd
  3. Nov 3, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    Assuming [itex]G^{-1}[/itex] exists and is a 1:1 map, then yes....Some functions do not have inverses that uniquely determine y(x), for instance [itex]y^2(x)=F(x)+C \Rightarrow y(x)= \pm \sqrt{F(x)+C}[/itex] which is not a single valued function.
  4. Nov 3, 2008 #3
    hello, I'm also taking a class on ODE but i have a problem -i use An Intro course in Diff. eq.'s by Zill - that i get a nonsense result here is the eq:

    sin3x + 2y(cos3x)^3 = 0 (here ^ is to raise a power.how are u raising powers & all the mathematical writings?)

    the eq in standard form look: (y^2)'=2ydy= -sin3x dx/2(cos 3x)^3.

    the last result i get which is nonsense ofcourse is: y^2 = -1/6(cos3x)^2. another result includes tan3x but is still negative.

    so y^2 is negative which is impossible. is the result right? I think there's a problem with the D.E. given.

    hope u can help. thx
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Separable Differential Equations Date
Arbitrary constant in denominator Oct 28, 2016
Separable Differential Equation Sep 25, 2016
Separable differential equation Sep 25, 2016
Another Diff Eq's one: am I wrong? Jul 18, 2015
Differential Equations, Separable, Simplification of answer Jun 29, 2015