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Need Help with Integration for Solving ODE

  1. Mar 31, 2016 #1
    1. The problem statement, all variables and given/known data
    [tex]\frac{dy}{dx}=y^2-1[/tex]
    [tex]y(0)=3[/tex]

    2. Relevant equations
    [tex]\frac{dy}{dx}=f(y) \leftrightarrow \frac{dx}{dy}=\frac{1}{f(y)}[/tex]

    3. The attempt at a solution
    [tex]\frac{dx}{dy}=\frac{1}{y^2-1}[/tex]
    [tex]dx=\frac{dy}{y^2-1}[/tex]
    [tex]\int dx=\int \frac{dy}{y^2-1}+C[/tex]
    [tex]x=\int \frac{dy}{y^2-1}+C[/tex]
    How do I integrate [itex]\int \frac{dy}{y^2-1}[/itex]?
     
  2. jcsd
  3. Mar 31, 2016 #2

    Mark44

    Staff: Mentor

    Partial fractions. See https://www.physicsforums.com/insights/partial-fractions-decomposition/ if you are uncertain about this technique.
     
  4. Mar 31, 2016 #3
    Hi Mad:

    I will give you a hint. think about factoring y2-1 = f1(y) × f2(y).
    Then think about finding A and B such that 1/(f1 × f2) = A/f1 + B/f2.

    Hope this helps.

    Regards,
    Buzz
     
  5. Mar 31, 2016 #4
    Thanks, I got the answer.
     
  6. Mar 31, 2016 #5

    epenguin

    User Avatar
    Homework Helper
    Gold Member

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