Use an appropriate substitution to solve the equation y --y y4 and find the solution that satisfies y(1) = 1. y(x) =

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(æ)y".
dx
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— п)P(#)и %3 (1 — п)Q(2).
dx
Use an appropriate substitution to solve the equation
y4
y' –
714 '
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(æ)y". dx 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— п)P(#)и %3 (1 — п)Q(2). dx Use an appropriate substitution to solve the equation y4 y' – 714 ' and find the solution that satisfies y(1) = 1. y(x) =
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