Techniques for solving various differential equations

[JD88]

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 I've 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 won't bother putting too many specific examples.

Thanks in advance, and I look forward to reading your responses.

 

[CFDFEAGURU]

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.

Thanks
Matt