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First order separable differential equation

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

    [tex]\frac{dy}{dx} + x^{2} = x[/tex]

    2. Relevant equations

    Above.

    3. The attempt at a solution


    After rearranging, I am stuck at

    [tex]\int \frac{1}{x-x^{2}} dx = \int dt[/tex]

    I can't think of any u-substitution, or any other trick for integrals I could use to solve this.
     
  2. jcsd
  3. Feb 1, 2008 #2
    Recheck you're expressions. The problem you give involves x and y, while the attempt at a solution gives x and t. Please clarify.

    It looks like you should have dx/dt where you currently have dy/dx no? If that's the case consider a partial fraction decomposition.
     
  4. Feb 1, 2008 #3
    I wrote the wrong variable for the last integral. It should have been of dy rather than dt. I solved it. I forgot about partial fractions.
     
  5. Feb 1, 2008 #4

    HallsofIvy

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    Even so, [itex]dy/dx= x- x^2[/itex] becomes [itex]dy= (x- x^2)dx[/itex]. There is no need for partial fractions.
     
  6. Feb 1, 2008 #5
    What need to find if y, then
    [tex]y=\int(x-x^2)dx=\frac{x^2}{2}-\frac{x^3}{3}+C[/tex]
     
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