3. a. Assume that P(x) and Q(x) are continuous over the interval [a, b]. Use the Fundamental Theorem of Calculus, Part 1, to show that any function y satisfying the equation | v(x)Q\x). dx + C v(x)y = for v(x) = eſ P(x) dx is a solution to the first-order linear equation dy + P(x) у 3D 0(х). dx b. If C = yov(xo) – J, v(t)Q(t) dt, then show that any solution y in part (a) satisfies the initial condition y(xo) = yo-

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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3. a. Assume that P(x) and Q(x) are continuous over the interval
[a, b]. Use the Fundamental Theorem of Calculus, Part 1, to
show that any function y satisfying the equation
| v(x)Q\x).
dx + C
v(x)y =
for v(x) = eſ P(x) dx is a solution to the first-order linear equation
dy
+ P(x) у 3D 0(х).
dx
b. If C = yov(xo) – J, v(t)Q(t) dt, then show that any solution
y in part (a) satisfies the initial condition y(xo) = yo-
Transcribed Image Text:3. a. Assume that P(x) and Q(x) are continuous over the interval [a, b]. Use the Fundamental Theorem of Calculus, Part 1, to show that any function y satisfying the equation | v(x)Q\x). dx + C v(x)y = for v(x) = eſ P(x) dx is a solution to the first-order linear equation dy + P(x) у 3D 0(х). dx b. If C = yov(xo) – J, v(t)Q(t) dt, then show that any solution y in part (a) satisfies the initial condition y(xo) = yo-
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