Answered: Figure 1.5.8 shows a slope field and…

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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Figure 1.5.8 shows a slope field and typical solution curves for the equation . (a) Show that every solution curve approaches the straight line y= -x - 1 as x goes to negative infinity. (b) For each of the five values y sub1 = -10, -5, 0, 5, and 10, determine the initial value (accurate to five decimal places) such that y(5) = y sub1for the solution satisfying the initial condition y(-5) = y sub0.

Image: Slope field and solution curves for y' = x + y

Expert Solution

Step 1

$G i v e n : D i f f e r e n t i a l e q u a t i o n i s y^{1} = y + x T o S h o w : a) S h o w t h a t s o l u t i o n o f t h e d i f f e r e n t i a l e q u a t i o n a p p r o a c h e s t h e s t r a i g h t l i n e y = - x - 1 w h e n x \to \infty b) D e t e r m i n e t h e i n i t i a l v a l u e s u c h t h a t y (5) = y_{1} a n d y_{1} = - 10, - 5, 0, 5, 10$