Plotting the slope field of an ode

y'=x^2+y^2-1     (Problem 1.3.23)

<< Graphics`PlotField`

a = 
      PlotVectorField[{1, x^2 + y^2 - 1}, {x, -4, 4}, {y, -4, 4},  
        Axes -> True]

If y(0)=0, then what is y(2)?

Answer:  About 1.

soln = 
      NDSolve[{y'[x] == x^2 + y[x]^2 - 1, y[0] == 0}, 
        y, {x, 0, 2}]

b = 
      Plot[Evaluate[ y[x]  /.  soln], {x, 0, 2},  
        PlotRange -> All]

Show[a, b]

y[2] /.  soln