Differential Equations - dy/dx = g(y)
An equation that involves independent variables, dependent variables, derivatives of the dependent variables with respect to independent variables, and constant is called a differential equation.
The case of is very similar to the method of We will look at some examples in a moment, but in this case we may need a little bit more rearranging and algebra involved.
Differential Equation of the Form
Let's look at some examples:
If express in terms of
This differential equation is separable—we can move the and around and then integrate both sides to find a general solution.
Multiply both sides by and divide by which gives us Now, taking the integral of both sides, we have which now becomes the following if we integrate: and by rearranging we get
If express in terms of
Again this is separable, so we can do the same as in the previous example, by multiplying both sides by and dividing by Taking the integral of both sides gives which now becomes the following if we integrate: and we can now rearrange to get