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48. (a) Show that y(x) = Cx* defines a one-parameter fam- ily of differentiable solutions of the differential equation xy' = 4y (Fig. 1.1.9). (b) Show that (-x* if x < 0, У(х) 3D I x* if x 20 defines a differentiable solution of xy' = 4y for all x, but is not of the form y(x) = Cxª. (c) Given any two real num- bers a and b, explain why-in contrast to the situation in part (c) of Problem 47–there exist infinitely many differ- entiable solutions of xy' = 4y that all satisfy the condition y(a) = b. 100 80 60 40 20 -20 -40 -60 -80 -100 -5 -4 -3 -2 -1 01 2 3 4 5 FIGURE 1.1.9. The graph y = Cx* for various values of C.

48. (a) Show that y(x) = Cx* defines a one-parameter fam- ily of differentiable solutions of the differential equation xy' = 4y (Fig. 1.1.9). (b) Show that (-x* if x < 0, У(х) 3D I x* if x 20 defines a differentiable solution of xy' = 4y for all x, but is not of the form y(x) = Cxª. (c) Given any two real num- bers a and b, explain why-in contrast to the situation in part (c) of Problem 47–there exist infinitely many differ- entiable solutions of xy' = 4y that all satisfy the condition y(a) = b. 100 80 60 40 20 -20 -40 -60 -80 -100 -5 -4 -3 -2 -1 01 2 3 4 5 FIGURE 1.1.9. The graph y = Cx* for various values of C.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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48. (a) Show that y(x) = Cx* defines a one-parameter fam- ily of differentiable solutions of the differential equation xy' = 4y (Fig. 1.1.9). (b) Show that (-x* if x < 0, У(х) 3D I x* if x 20 defines a differentiable solution of xy' = 4y for all x, but is not of the form y(x) = Cxª. (c) Given any two real num- bers a and b, explain why-in contrast to the situation in part (c) of Problem 47–there exist infinitely many differ- entiable solutions of xy' = 4y that all satisfy the condition y(a) = b. 100 80 60 40 20 -20 -40 -60 -80 -100 -5 -4 -3 -2 -1 01 2 3 4 5 FIGURE 1.1.9. The graph y = Cx* for various values of C.
Transcribed Image Text:48. (a) Show that y(x) = Cx* defines a one-parameter fam- ily of differentiable solutions of the differential equation xy' = 4y (Fig. 1.1.9). (b) Show that (-x* if x < 0, У(х) 3D I x* if x 20 defines a differentiable solution of xy' = 4y for all x, but is not of the form y(x) = Cxª. (c) Given any two real num- bers a and b, explain why-in contrast to the situation in part (c) of Problem 47–there exist infinitely many differ- entiable solutions of xy' = 4y that all satisfy the condition y(a) = b. 100 80 60 40 20 -20 -40 -60 -80 -100 -5 -4 -3 -2 -1 01 2 3 4 5 FIGURE 1.1.9. The graph y = Cx* for various values of C.
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