2.2.3-4 #3a Solve the differential equation by conversion to polar coordinates and sketch the solution curves:

Solution: 1. Rewrite equation in standard differential form:

2. Equation is homogeneous. Use conversion to polar coordinates to reduce it to separable ODE

3.

> restart;

> with(plots):

> P:={seq((c/2)*exp(t),c=-4..4)}:

> polarplot(P,t=-1.5*Pi..1.5*Pi,color=black,view=[-4..4,-4..4]);