1st order DE

1st order DE

1. Method of Solution

   • Separable eq
     • separate v&x
       • integrate both side
   • Homogenous eq
     • determine the eq
       • sub (y=vx) and (dy/dx=v+x dv/dx)
   • Exact DE
     • M dy + N dx = 0
       • • if exact
           • M= , N=
             • u(x,y) = M(x,y) dx +
               • u(x,y) = N(x,y) dy +
                 • compare
         • if not exact
   • Linear
   • Bernoulli eq
   • Solutions by Subtitution
   • Autonomous eq

2. Applications

   • Newton's Law of cooling
   • Natural Growth & Decay
   • Electric Circuits Model
   • Vertical Motion