(a) Use the direction field of Problem 6 to estimate the values at x = 2 of the two solutions of the differential equation y′ = x − y + 1 with initial values y(−3) = −0.2 and y(−3) = + 0.2.
(b) Use a computer algebra system to estimate the values at x = 3 of the two solutions of this differential equation with initial values y(−3) = −0.5 and y(−3) = + 0.5.
The lesson of this problem is that big changes in initial conditions may make only small differences in results.
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