01
Integral curves of homogeneous equation
Consider the integral curves of a homogeneous equation. Take a straight line through the origin. Show that this line crosses all the integral curves at the same angle of intersection.
02
First-order families
The family of curves solving a first-order linear differential equation has the general form . Now suppose we start with a family of curves in this form. Find the differential equation corresponding to this family and show that it is first-order linear.