A Bernoulli differential equation is one of the form dy + P(z)y = Q(1)y". dz 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 %3! du + (1 - п)lР(l)и 3 (1- п)0 (+l. dz Use an appropriate substitution to solve the equation 4 y3 and find the solution that satisfies y(1) = 1. y(x) =
A Bernoulli differential equation is one of the form dy + P(z)y = Q(1)y". dz 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 %3! du + (1 - п)lР(l)и 3 (1- п)0 (+l. dz Use an appropriate substitution to solve the equation 4 y3 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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Transcribed Image Text:A Bernoulli differential equation is one of the form
dy
+ P(z)y = Q(r)y".
dz
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(z)u = (1 – n)Q(z).
dz
Use an appropriate substitution to solve the equation
4
y3
and find the solution that satisfies y(1) = 1.
y(z) =
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