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olve a nonlinear equation by making a change of the dependent var portant such equation has the form y + p(t)y = q(t)y" ation after Jakob Bernoulli. ution v = y reduces Bernoulli's equation to a linear equation. uation by using this substitution. fy +7ty - y = 0,1 > 0 14

olve a nonlinear equation by making a change of the dependent var portant such equation has the form y + p(t)y = q(t)y" ation after Jakob Bernoulli. ution v = y reduces Bernoulli's equation to a linear equation. uation by using this substitution. fy +7ty - y = 0,1 > 0 14

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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Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear equation. The most important such equation has the form y + p(t)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. Ifn + 0, 1, then the substitution v = y-" reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. fy +7ty – y = 0,1 > 0 %3D y = ± + ct14 15t y = ± + cıl4 15t 2 y = ± + cil4 15t 1 y = ± + ct? 81 y = + + ci? 8t
Transcribed Image Text:Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear equation. The most important such equation has the form y + p(t)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. Ifn + 0, 1, then the substitution v = y-" reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. fy +7ty – y = 0,1 > 0 %3D y = ± + ct14 15t y = ± + cıl4 15t 2 y = ± + cil4 15t 1 y = ± + ct? 81 y = + + ci? 8t
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