Figure 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 = −10, −5, 0, 5, and 10, determine the initial value y0 (accurate to five decimal places) such that y(5) = y1 for the solution satisfying the initial condition y(−5) = y0.
FIGURE. Slope field and solution curves for y′ = x + y.
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