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A Bernoulli differential equation is one of the form dy dr Use an appropriate substitution to solve the equation + P(x)y=Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹ transforms the Bernoulli equation into the linear equation du +(1-n)P(x)u = (1-n)Q(x). da 7 1-y= 214

A Bernoulli differential equation is one of the form dy dr Use an appropriate substitution to solve the equation + P(x)y=Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹ transforms the Bernoulli equation into the linear equation du +(1-n)P(x)u = (1-n)Q(x). da 7 1-y= 214

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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A Bernoulli differential equation is one of the form Use an appropriate substitution to solve the equation dy de Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹-" transforms the Bernoulli equation into the linear equation du da and find the solution that satisfies y(1) = 1. y(x) = + P(x)y= Q(x)y". + (1 − n)P(x)u = (1 − n)Q(x). y - 7 -y= 14'
Transcribed Image Text:A Bernoulli differential equation is one of the form Use an appropriate substitution to solve the equation dy de Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹-" transforms the Bernoulli equation into the linear equation du da and find the solution that satisfies y(1) = 1. y(x) = + P(x)y= Q(x)y". + (1 − n)P(x)u = (1 − n)Q(x). y - 7 -y= 14'
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