Differential Equations

We are asked to find the differential equation of all circles with radius

a

. A circle's equation can be written as:

(x%20-%20h)%5E2%20%2B%20(y%20-%20k)%5E2%20%3D%20a%5E2

where

(h%2C%20k)

is the center and

a

is the radius.
Step 1:
Implicitly differentiate the equation of the circle twice with respect to

x

.
Step 2:
First differentiation gives the first derivative

%5Cfrac%7Bdy%7D%7Bdx%7D

, and the second differentiation gives

%5Cfrac%7Bd%5E2%20y%7D%7Bdx%5E2%7D

.
Step 3:
After applying the differentiation process, we arrive at the differential equation:

%5Cleft(%201%20%2B%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cright)%5E3%20%3D%20a%5E2%20%5Cleft(%20%5Cfrac%7Bd%5E2%20y%7D%7Bdx%5E2%7D%20%5Cright)%5E2

Chapter Questions
1 MCQs