Figure 1.5.7 shows a slope field and typical solution curves for the equation y' = x - y.

(a) Show that every solution curve approaches the straight line y = x - 1 as x → + ∞.

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

Transcribed Image Text:

10 8 6 4 -2 -4 -6 -8 -10 -5 F 1114 0 x 1111 111 71 11 // 1 5 FIGURE 1.5.7. Slope field and solution curves for y' = x - y.