(a) Use the direction field of Problem 5 to estimate the values at x = 1 of the two solutions of the differential equation y′ = y − x + 1 with initial values y(−1) = −1.2 and y(−1) = −0.8.
(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) = −3.01 and y(−3) = −2.99.
The lesson of this problem is that small changes in initial conditions can make big differences in results.
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