1. Not finding help here? Sign up for a free 30min 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!

Problem solving separable diff EQ w/ I.Condition. , they say its wrong :x

  1. Jan 14, 2006 #1
    Hello everyone i did this one surley thing it would work out and yet another failure. :cry:
    Solve the separable differential equation
    11 x - 8 y*sqrt{x^2 + 1}*{dy}/{dx} = 0.
    Subject to the initial condition: y(0) = 6.
    y = ?


    I'm pretty sure where I messed up is when i tried to solve for y, i htink i screwed up there but i'm not sure, anyone know? Thanks! its #11. Ignore that top stuff please!

    Here is my work:
    [​IMG]
     
  2. jcsd
  3. Jan 14, 2006 #2

    benorin

    User Avatar
    Homework Helper

    Particular solution

    You problem lies in where you placed your constant of integration, namely:

    [tex]11\int \frac{x}{\sqrt{x^2+1}}dx = \frac{11}{2}\int \frac{1}{\sqrt{u}}du = \frac{11}{2}\int u^{-\frac{1}{2}}du = 11u^{\frac{1}{2}}+C=11\sqrt{x^2+1}+C[/tex]

    C is outside the square root, from there

    [tex]4y^2=11\sqrt{x^2+1}+C[/tex]

    [tex]y^2=\frac{11}{4}\sqrt{x^2+1}+\frac{C}{4}[/tex]

    or,

    [tex]y=\pm\sqrt{\frac{11}{4}\sqrt{x^2+1}+\frac{C}{4}}[/tex]

    to solve for C, use the simplest form of the solved DE, that is use

    [tex]4y^2=11\sqrt{x^2+1}+C[/tex]

    for x=0 and y(0)=6, this gives

    [tex]4(6)^2=11\sqrt{0^2+1}+C[/tex]

    which simplifies to

    [tex]144=11+C[/tex]

    and hence C=133, plug this into

    [tex]y=\pm\sqrt{\frac{11}{4}\sqrt{x^2+1}+\frac{C}{4}}[/tex]

    to get

    [tex]y(x)=\pm\sqrt{\frac{11}{4}\sqrt{x^2+1}+\frac{133}{4}}=\pm\frac{1}{2}\sqrt{11\sqrt{x^2+1}+133}[/tex]

    as your particular solution.
     
    Last edited: Jan 14, 2006
  4. Jan 15, 2006 #3
    yup, that constant shouldn't be under the radical! :tongue:
     
  5. Jan 15, 2006 #4
    Ahhh, that worked perfectly Benorin, thanks a ton (again)! :) The step by step explanation is great!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Problem solving separable diff EQ w/ I.Condition. , they say its wrong :x
  1. Solve this diff eq. (Replies: 6)

  2. Diff. Eq. Solve (Replies: 11)

Loading...