In Example 7 we saw that y.x/ D 1=.C ! x/ denes a one-parameter family of solutions of
Chapter 3, Problem 47(choose chapter or problem)
In Example 7 we saw that y.x/ D 1=.C ! x/ denes a one-parameter family of solutions of the differential equation dy=dx D y2. (a) Determine a value of C so that y.10/D 10. (b) Is there a value of C such that y.0/D 0? Can you nevertheless nd by inspection a solution of dy=dx D y2 such that y.0/ D 0? (c) Figure 1.1.8 shows typical graphs of solutions of the form y.x/D 1=.C !x/. Does it appear that these solution curves ll the entire xyplane? Can you conclude that, given any point .a;b/ in the plane, the differential equation dy=dx D y2 has exactly one solution y.x/satisfying the condition y.a/Db?
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