Math 224-01: Differential Equations: Reading Homework 1.7

1. Planar Systems and First Order ODEs : what change in the ODEs we consider is introduced in this section?
   
   1. Systems : what is the state-space of a first-order planar differential system? what does autonomous mean?
      
      1. systems and solution curves : how can solution curves to the ODE N(x,y) y'(x) + M(x,y) = 0 be plotted? why?
         
   2. Reduction of order : what is the idea behind reduction of order?
      
      1. y''=F(t,y') : how can we solve second-order differential equations of this form?
         
      2. y''=F(y,y') : how can we solve second-order differential equations of this form?