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3. A solution of a'c(x.1) ax? ac(x,1) at is the function c(x, 1) = 47 Dt 4Dt for xeR and r > 0. (a Show that, as a function of x for fixed values of t > 0, c(x, 1) is (i) positive for all xe R, (ii) is increasing for x < 0 and decreas- ing for x > 0, (iii has a local maximum at x = 0, and (iv) has inflection points at x =±/2Di.

3. A solution of a'c(x.1) ax? ac(x,1) at is the function c(x, 1) = 47 Dt 4Dt for xeR and r > 0. (a Show that, as a function of x for fixed values of t > 0, c(x, 1) is (i) positive for all xe R, (ii) is increasing for x < 0 and decreas- ing for x > 0, (iii has a local maximum at x = 0, and (iv) has inflection points at x =±/2Di.

Advanced Engineering Mathematics
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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3. A solution of ac(x.1) a'c(x.1) D ax? at is the function c(x, 1) = exp 47 DI 4Dt for xeRand r> 0. (a Show that, as a function of x for fixed values of t > 0, c(x.1) is (i) positive for all x e R, (ii) is increasing for x < 0 and decreas- ing for x > 0, (ii) has a local maximum at x = 0, and (iv) has inflection points at x =+/2D1. (b) Graph c(x.r) as a function of x when D 1 for t 0.01. 1 = 0.1, and r = 1.
Transcribed Image Text:3. A solution of ac(x.1) a'c(x.1) D ax? at is the function c(x, 1) = exp 47 DI 4Dt for xeRand r> 0. (a Show that, as a function of x for fixed values of t > 0, c(x.1) is (i) positive for all x e R, (ii) is increasing for x < 0 and decreas- ing for x > 0, (ii) has a local maximum at x = 0, and (iv) has inflection points at x =+/2D1. (b) Graph c(x.r) as a function of x when D 1 for t 0.01. 1 = 0.1, and r = 1.
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