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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 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

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-" reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. t²y + 7ty-y³ = 0,t> 0 1 y = ± + ct¹4 15t 2 y = ± + ct¹4 15t y = ± y = ± y = ± O O O 15t √√=+² ct¹ + ct7 + + ct¹4 14 -
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-" reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. t²y + 7ty-y³ = 0,t> 0 1 y = ± + ct¹4 15t 2 y = ± + ct¹4 15t y = ± y = ± y = ± O O O 15t √√=+² ct¹ + ct7 + + ct¹4 14 -
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