MAT252 Spring 2008. Separation of Variables. General Information. Some differential equations can be solved by the method of separation of variables (or "variables separable") . This method is only possible if we can write the differential equation in the form A(x) dx + B(y) dy = 0,
Separation of Variables
A(x) dx + B(y) dy = 0,
where A(x) is a function of x only and B(y)
is a function of y only.
Separation of variables can be used to solve:
We can integrate this immediately:
If needed, you could solve for y explicitly. K is a constant.
1. Separate the variables (a little algebra here) to get:
2. Integrate both sides:
Separating the variables:
Some more algebra gives us:
Integration by parts (left-hand side) and an easy integration on the right-hand side:
Still have questions?? Ask in class!!