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A Bernoulli differential equation is one of the form dy + P(x)y = Q(x)y". da Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du + (1 - n)P(x)u = (1- n)Q(x). da Use an appropriate substitution to solve the equation xy' + y = -8xy?, and find the solution that satisfies y(1) = 1. y(x)

A Bernoulli differential equation is one of the form dy + P(x)y = Q(x)y". da Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du + (1 - n)P(x)u = (1- n)Q(x). da Use an appropriate substitution to solve the equation xy' + y = -8xy?, and find the solution that satisfies y(1) = 1. y(x)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A Bernoulli differential equation is one of the form dy + P(x)y Q(x)y". dx Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = n transforms the Bernoulli equation into the linear equation du + (1 – n)P(x)u dx = (1 – n)Q(x). Use an appropriate substitution to solve the equation xy + y = = -8zy, and find the solution that satisfies y(1) = 1. y(x)
Transcribed Image Text:A Bernoulli differential equation is one of the form dy + P(x)y Q(x)y". dx Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = n transforms the Bernoulli equation into the linear equation du + (1 – n)P(x)u dx = (1 – n)Q(x). Use an appropriate substitution to solve the equation xy + y = = -8zy, and find the solution that satisfies y(1) = 1. y(x)
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