+ (1—п)P(х)и %3D (1 — п)Q("). dx Use an appropriate substitution to solve the equation 6 -y = æ14

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(г)у —
dx
Q(x)y".
Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y
transforms the Bernoulli equation into the linear
equation
du
+ (1 — п)Р(«)и 3 (1 — п)Q(2).
dx
Use an appropriate substitution to solve the equation
6
y'
x14 '
and find the solution that satisfies y(1) = 1.
у(х) — (5х^(18/(-3x^5+8))
Transcribed Image Text:A Bernoulli differential equation is one of the form dy + P(г)у — dx Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y transforms the Bernoulli equation into the linear equation du + (1 — п)Р(«)и 3 (1 — п)Q(2). dx Use an appropriate substitution to solve the equation 6 y' x14 ' and find the solution that satisfies y(1) = 1. у(х) — (5х^(18/(-3x^5+8))
Expert Solution
Step 1

Introduction:

The solution to the differential equation of the form y'+p(x)y=q(x) is given by,

y(I.F.)=q(x)(I.F.)dx+c

Where (I.F.) is integrating factor given by,

I.F.=ep(x)dx

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