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Solve the initial value problem

  1. Oct 8, 2007 #1
    1. The problem statement, all variables and given/known data
    Solve the initial value problem given x(2)=0

    [tex]\frac{dx}{dt}=tx^{2}+2x^{2}t^{2}[/tex]


    2. Relevant equations



    3. The attempt at a solution
    I factored out the x^2 and separated variables and integrated as follows:

    [tex]\int\frac{dx}{x^{2}} = \int t+2t^{2} dt[/tex]

    [tex]\frac{-1}{x}=\frac{1}{2}t^{2}+\frac{2}{3}t^{3} + C[/tex]


    Which is simple enough, but I get really confused when solving for C. Trying to solve from the equation above divides by zero and the world ends- rearranging explicitly for x doesn't do me any good either. Suggestions on where to go from here?
     
  2. jcsd
  3. Oct 8, 2007 #2

    Dick

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    Homework Helper

    This may seem like kind of a cheat, but x(t)=0 for all t is also a solution.
     
  4. Oct 8, 2007 #3
    Thanks for that, I didn't think of that case. If something similar shows up on the exam I'll always check for something like that
     
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