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Solve the given Bernoulli equation by using this substitution. 1 ty' + 4ty - y³ = 0,t > 0

Solve the given Bernoulli equation by using this substitution. 1 ty' + 4ty - y³ = 0,t > 0

Advanced Engineering Mathematics
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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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
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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