Solution Found!
have the same domain but are clearly different. See
Chapter 1, Problem 50E(choose chapter or problem)
The functions \(y(x)=\frac{1}{16} x^{4}, \ \ -\infty<x<\infty\) and \(y(x)=\left\{\begin{array}{ll} 0, & x<0 \\\frac{1}{16} x^{4}, & x \geq 0 \end{array}\right.\)
have the same domain but are clearly different. See Figures 1.2.12(a) and 1.2.12(b), respectively. Show that both functions are solutions of the initial-value problem \(d y / d x=x y^{1 / 2}\), y(2) = 1 on the interval \((-\infty, \infty)\). Resolve the apparent contradiction between this fact and the last sentence in Example 5.
Text Transcription:
y(x)=1/16 x^4, -infty<x<infty
y(x)={0, x<0 over 1/16 x^4, x geq 0
dy/dx=xy^1/2
(-infty, infty)
Questions & Answers
QUESTION:
The functions \(y(x)=\frac{1}{16} x^{4}, \ \ -\infty<x<\infty\) and \(y(x)=\left\{\begin{array}{ll} 0, & x<0 \\\frac{1}{16} x^{4}, & x \geq 0 \end{array}\right.\)
have the same domain but are clearly different. See Figures 1.2.12(a) and 1.2.12(b), respectively. Show that both functions are solutions of the initial-value problem \(d y / d x=x y^{1 / 2}\), y(2) = 1 on the interval \((-\infty, \infty)\). Resolve the apparent contradiction between this fact and the last sentence in Example 5.
Text Transcription:
y(x)=1/16 x^4, -infty<x<infty
y(x)={0, x<0 over 1/16 x^4, x geq 0
dy/dx=xy^1/2
(-infty, infty)
ANSWER:Step 1 of 5
Given that
We have to show that both functions are solutions of the initial-value problem.