Graphical Properties of Solution Curves

At any point on a differentiable solution curve, there is a unique tangent line that represents the value of $dy/dx$ at that point.

A solution curve can intersect itself at more than one point in a well-posed differential equation, providing multiple tangent directions at an intersection.

Distinct solution curves corresponding to different initial conditions do not intersect due to the uniqueness theorem.

Graphical methods such as slope fields offer valuable insights into the qualitative behavior of differential equations even when analytic solutions are difficult to obtain.