Geometric view of Differential Equations
In Differential Equations, one can sometime solve them using analytic methods (such as separation by parts). But this is not that common. An alternative approach, for an ODE, is to plot the slopes across the plane where the DE is defined (using isocline or computational methods).
Figure 1: This shows the slopes across the DE field of \( \dot y = xy \) as well as the isoclines in blue. Solution (integral) curves are shown in red.
1. Associated Notes