Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it in equation. The most important such equation has the form y' + p(t)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. fn 0, 1, then the substitution v = yl-n reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. ty' + 4ty - y³ = 0,t> 0
Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it in equation. The most important such equation has the form y' + p(t)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. fn 0, 1, then the substitution v = yl-n reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. ty' + 4ty - y³ = 0,t> 0
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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![Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear
equation. The most important such equation has the form
y' + p(t)y = q(t)y"
and is called Bernoulli's equation after Jakob Bernoulli.
If n
0, 1, then the substitution v = yl-n reduces Bernoulli's equation to a linear equation.
Solve the given Bernoulli equation by using this substitution.
ty' + 4ty - y³ = 0, t > 0
y = ±
+ ct8
y = ±
O
O
O
O
O
+1
y = ±
y = ±
2
+ Ct8
5t
+ ct4
1
+ ct4
+ ct
5t
9t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F928c89c9-5a28-4a50-b11e-a9311355e36e%2F78e37447-e0c2-4b60-bf78-49f5975ff626%2Fq1t98_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear
equation. The most important such equation has the form
y' + p(t)y = q(t)y"
and is called Bernoulli's equation after Jakob Bernoulli.
If n
0, 1, then the substitution v = yl-n reduces Bernoulli's equation to a linear equation.
Solve the given Bernoulli equation by using this substitution.
ty' + 4ty - y³ = 0, t > 0
y = ±
+ ct8
y = ±
O
O
O
O
O
+1
y = ±
y = ±
2
+ Ct8
5t
+ ct4
1
+ ct4
+ ct
5t
9t
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