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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(1)y" %3D and is called Bernoulli's equation after Jakob Bernoulli. Ifn + 0, 1, then the substitution v = y-ª reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. Py + 5ty – y = 0, t > 0 y = ± + ct 6t 2 + ct10 Ilt y = ± 1 y = ± + ci10 1 y = ± + ct5 2 + ct'0 11t y = ± |-lö

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(1)y" %3D and is called Bernoulli's equation after Jakob Bernoulli. Ifn + 0, 1, then the substitution v = y-ª reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. Py + 5ty – y = 0, t > 0 y = ± + ct 6t 2 + ct10 Ilt y = ± 1 y = ± + ci10 1 y = ± + ct5 2 + ct'0 11t y = ± |-lö

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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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(1)y" %3D and is called Bernoulli's equation after Jakob Bernoulli. Ifn + 0, 1, then the substitution v = y-ª reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. Py + 5ty – y = 0, t > 0 y = ± + ct 6t 2 + ct10 Ilt y = ± 1 y = ± + ci10 1 y = ± + ct5 2 y = ± + cr!0 11t |-lö
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(1)y" %3D and is called Bernoulli's equation after Jakob Bernoulli. Ifn + 0, 1, then the substitution v = y-ª reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. Py + 5ty – y = 0, t > 0 y = ± + ct 6t 2 + ct10 Ilt y = ± 1 y = ± + ci10 1 y = ± + ct5 2 y = ± + cr!0 11t |-lö
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