Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear quation. 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-" reduces Bernoulli's equation to a linear equation. olve the given Bernoulli equation by using this substitution. t²y + 7ty-y³ = 0,t> 0 y = ± + ct¹4 2 y = ± +q¹4 15t y = ± y = ± y = ± O O O O O +c¹4 + ct¹
Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear quation. 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-" reduces Bernoulli's equation to a linear equation. olve the given Bernoulli equation by using this substitution. t²y + 7ty-y³ = 0,t> 0 y = ± + ct¹4 2 y = ± +q¹4 15t y = ± y = ± y = ± O O O O O +c¹4 + ct¹
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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