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Techniques for solving various differential equations

  1. Sep 19, 2009 #1
    So I have recently begun my first graduate level engineering math class. The course teaches us different techniques for solving various differential equations. Many of these equations I have never actually seen being applied to something, they are only just examples for us to learn how to solve them. So I am curious what kind of physical systems these equations model.

    For example:
    Bernoulli Differential Equations
    Ricatti Equation
    Euler-Cauchy Equations

    Many of the other equations are just first order equation that are unlike any Ive seen be applied to something in my courses before. Such as...

    x (x^2+y^2) dy/dx = y^3

    dy/dx = (x+y) / (x-y)

    There are many more but I wont bother putting too many specific examples.

    Thanks in advance, and I look forward to reading your responses.
  2. jcsd
  3. Sep 19, 2009 #2
    Re: Applications?

    Ordinary differential equations are used in every field of science.

    Euler-Cauchy Equations are used in fluid mechanics and various other places. Same for the Bernoulli equation. I don't have a good example for the Ricatti equation.

    x (x^2+y^2) dy/dx = y^3

    dy/dx = (x+y) / (x-y)

    These equations are just equations for you to solve. They don't represent anything in particular. When you solve them you will have a constant, c, in the result and you can't proceed any further unless information is provided such as, an initial value.

    Last edited: Sep 19, 2009
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