Figure 1.5.8 shows a slope field and typical solution curves for the equation y' = x + y. (a) Show that ev- ery solution curve approaches the straight line y = -x – 1 as x → -00. (b) For each of the five values yı = -10, -5, 0, 5, and 10, determine the initial value yo (accurate to five decimal places) such that y(5) = yı for the solution satisfying the initial condition y(-5) = yo- 10 6. 2 -10 -5 FIGURE 1.5.8. Slope field and solution curves for y' = x + y.
Figure 1.5.8 shows a slope field and typical solution curves for the equation y' = x + y. (a) Show that ev- ery solution curve approaches the straight line y = -x – 1 as x → -00. (b) For each of the five values yı = -10, -5, 0, 5, and 10, determine the initial value yo (accurate to five decimal places) such that y(5) = yı for the solution satisfying the initial condition y(-5) = yo- 10 6. 2 -10 -5 FIGURE 1.5.8. Slope field and solution curves for y' = x + y.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Figure 1.5.8 shows a slope field and typical solution
curves for the equation y' = x + y. (a) Show that ev-
ery solution curve approaches the straight line y = -x – 1
as x → -00. (b) For each of the five values yı = -10,
-5, 0, 5, and 10, determine the initial value yo (accurate to
five decimal places) such that y(5) = yı for the solution
satisfying the initial condition y(-5) = yo-
10
6.
2
-10
-5
FIGURE 1.5.8. Slope field and solution curves
for y' = x + y.
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