Equations with separable variables

(Basic form)

To solve it:

1. Separate the variables y from x, i.e., by collecting on one side all terms involving y together with dy, while all terms involving x together with dx are put on the other side.

2. Integrate both sides.

3. If the solution can be defined explicitly, i.e., it can be solved for y as a function of x, then do it. If not, the solution can be defined implicitly, i.e., it cannot be solved for y as a function of x.

Examples 6. Solve the following differential equations:

Note:

1. Solutions for the above examples are called the general solutions.

2. The general solution for example 1 is defined explicitly, where as, the general solution for example 2 is defined implicitly.

3. If C is to be evaluated, then the solution is called the solution of the initial-value problem.

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