How is a differential equation different from a regular one? Well, the solution is a function (or a class of functions), not a number. How do you like me now (that is what the differential equation would say in response to your shock)!
Euler's method is a relatively simple numerical tool for approximating values for solutions of differential equations. It is based on the understanding that a function behaves similar to its tangent around the point where the tangent touches the function.
Exponential functions are described by differential equations of the general form dy/dx=ky, i.e. equations where the derivative is proportional to the function. Learn how to solve such equations and how to solve word problems with real-world contexts involving such equations.
In this equations, all of the fat is fully mixed in so it doesn't collect at the top. No (that would be homogenized equations).
Actually, the term "homogeneous" is way overused in differential equations. In this tutorial, we'll look at equations of the form y'=(F(y/x)).