5. The differential equation: + P(r)y= f(r)y", dr where n is any real number, is called a Bernoulli equation. The following steps will outline how to solve the Bernoulli equation: ry' + 2ry : I>0 (a) Rewrite the equation to match the general form outlined above. Find P(r), f(r), and n. (b) We will now use the substitution u = y'-" = y'-(-2) = y³ to rewrite the differential equation in terms of the du new dependent variable u. First, find dr (c) Now, multiply both sides of your differential equation from part (a) by 3y² and substitute u and du from part dr (b) into the differential equation.
5. The differential equation: + P(r)y= f(r)y", dr where n is any real number, is called a Bernoulli equation. The following steps will outline how to solve the Bernoulli equation: ry' + 2ry : I>0 (a) Rewrite the equation to match the general form outlined above. Find P(r), f(r), and n. (b) We will now use the substitution u = y'-" = y'-(-2) = y³ to rewrite the differential equation in terms of the du new dependent variable u. First, find dr (c) Now, multiply both sides of your differential equation from part (a) by 3y² and substitute u and du from part dr (b) into the differential equation.
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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How do I go about solving this with a Bernoulli equation?
Transcribed Image Text:5. The differential equation:
dy
dr
+ P(x)y = f(x)y",
where n is any real number, is called a Bernoulli equation. The following steps will outline how to solve the Bernoulli
equation:
ry' + 2ry
x >0
(a) Rewrite the equation to match the general form outlined above. Find P(x), f(x), and n.
(b) We will now use the substitution u = y'-" = y!-(-2) = y³ to rewrite the differential equation in terms of the
%3D
du
new dependent variable u. First, find
dr
(c) Now, multiply both sides of your differential equation from part (a) by 3y? and substitute u and
du
from part
d.r
(b) into the differential equation.
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