First Order, Separable

Differential Equations

Differential Equation mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders.

Let’s see some examples !

Solve the differential equation

and then solve the initial - value problem y (0) = 1

Practice Time!!!Solve the initial – value problem:

Slope FieldsFinding the solution given a differential

equation is often difficult.We can come up with a visual pattern for

the general solution graphically using slope fields.• Let’s take the differential equation

• Create a table showing several x, y, and y’ values:

x -2 -2 -1 -1 0 0 1 1 2 2

y -1 1 -1 1 -1 1 -1 1 -1 1

y’ -5 -5 -3 -3 -1 -1 1 1 3 3

Draw short segments represent y’ at the selected points.

We would need more points to give an accurate visual