Figure shows a slope field and typical solution curves for the equation y′ = x − y.xFIGURE...

Figure shows a slope field and typical solution curves for the equation y′ = x − y.

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FIGURE. Slope field and solution curves for y′ = x − y.

(a) Show that every solution curve approaches the straight line y − x − 1as x −> + ∞.

(b) For each of the five values yi = 3.998, 3.999, 4.000, 4.001, and 4.002, determine the initial value y() (accurate to four decimal places) such that y(5) = y1 for the solution satisfying the initial condition y(−5) = y0.