The Initial Value Problem y' = f(x, y) ; y(c) = d 11115
10
y(x) 5
0-2.5 -2 -1. 5 - 1 -0. (^5 0) 0.5
x
Figure 2.15 Numerical Approximation of the Solution to
y 1
y'= (x-l)(x+2) +;; y(-l)=^2
EXAMPLE 10 Numerical Approximation and Graph of the IVP:y' = -x/y; y(-1) = 1
Mathematically analyze the initia l value problem(28) y' = -x/y; y(-l) = 1
on the interval [-2, 2] taking into account the fundamental existence, unique-
ness, and continuation theorems. Then calculate and graph a numerical ap-
proximation of the solution to the IVP (28) using MAPLE.
SOLUTION
Mathematical Analysis
Here f(x,y) = -x/y and of joy= x/y^2 are defined and continuous on any
finite rectangle which does not contain any point (x, 0) - that is, on any finite