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What am I doing wrong? - Linear Differential Equations

  1. Oct 22, 2008 #1
    What am I doing wrong?? - Linear Differential Equations

    1. The problem statement, all variables and given/known data
    Hi everyone, the problem I have is listed under my attempt (I hope it's ok that I pasted it): to solve the below linear differential equation with the initial condition y(1)=1

    2. Relevant equations
    P(x) and Q(x) linear differential equation solution method


    3. The attempt at a solution
    [​IMG]
    [​IMG]

    Plugging in for 1=y and 1=x to solve for c has yielded me crazy results after i plugged in y^(-2). I got both c=6/7 and c=-1/6 but neither are the correct answer (this problem is listed on a program that allows me to check my answer) can anyone help me explain if I did a step wrong or if I am solving for C wrong??

    Thanks!
     
    Last edited: Oct 23, 2008
  2. jcsd
  3. Oct 23, 2008 #2

    HallsofIvy

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    Re: What am I doing wrong?? - Linear Differential Equations

    I don't know why you say "crazy results". If y= 1, then z= 1 also so your last equation becomes 1= 1/7 + C and C= 6/7 is the only result.

    y-2= -(1/7)x-4+ (6/7)x-18 gives

    [tex]y^2= \frac{1}{-(1/7)x^{-4}+ (6/7)x^{-18}}= \frac{-7}{x^{14}- 6}[/tex]
     
  4. Oct 23, 2008 #3
    Re: What am I doing wrong?? - Linear Differential Equations

    Well the crazy results come when i plug my answer into y=. The program keeps telling me that I am incorrect with
    [tex]\sqrt{7x^4}+((7x^{18})/6)[/tex]
    (that's to the 18th)
     
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