oulli’s equation, x' = a(t)x + f (t)x^n, n /= 0, 1, was proposed for solution by James Bernoulli in December 1695. In 1696, Leibniz pointed out that the equation can be reduced to a linear equation by taking x 1−n as the dependent variable. Show that the change of variable, z = x^1−n, will transform the nonli
oulli’s equation, x' = a(t)x + f (t)x^n, n /= 0, 1, was proposed for solution by James Bernoulli in December 1695. In 1696, Leibniz pointed out that the equation can be reduced to a linear equation by taking x 1−n as the dependent variable. Show that the change of variable, z = x^1−n, will transform the nonli
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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The presence of nonlinear terms prevents us from using
the technique of this section. In special cases, a change
of variable will transform the nonlinear equation into one
that is linear. The equation known as Bernoulli’s equation,
x' = a(t)x + f (t)x^n, n /= 0, 1,
was proposed for solution by James Bernoulli in December 1695. In 1696, Leibniz pointed out that the equation
can be reduced to a linear equation by taking x 1−n as the
dependent variable. Show that the change of variable,
z = x^1−n, will transform the nonlinear Bernoulli equation
into the linear equation
z' = (1 − n)a(t)z+(1−n)f(t)
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