1. Specialist Mathematics
Integral Calculus
Solving first-order differential equations.

2. Solving differential equations.
By separation of variables.
First order DEs with separable variables.
Examples:

3. To solve these equations we need to re-arrange them as
and integrate both sides of the equation.

4. Example 1: Solve
Hyperbolic slope fields show the solution
curve shape.

5. circle, centre (0,0), radius

6. Example 2: Show that the general solution to the differential equation
can be written as
Slope field shows
an exponential shape

7. Example 3: Solve the following differential equation
using integration by parts
is the general implicit solution
is the general solution

8. Solve the following DEs:
ANSWERS:

9. Watch the video: