Differential Equations are equations that involve a function and its derivatives. Sometimes they can be solved using a technique called separating variables. This only works for some differential equations.
Separable differential equations are equations of the form:
which can also be written as:
1. First we have to convert this to a separable differential equation. To do this multiply both sides by :
2. Multiply both sides by dx:
3. Integrate both sides:
(the C1 and C2 are arbitrary constants of integration):
4. Combine the arbitrary constants:
5. Take the negative reciprocal of both sides:
As you can see differential equations are separable if you can separate the variables and then integrate to solve.