Figure shows a slope field and typical solution curves for the equation y′ = x + y.(a) sho...

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.