Chapter 2, Section 2.4, Additional Question 04 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(i)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. If n + 0, 1, then the substitution v = y-" reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. Py + 5ty – y' = 0, t>0 y = + Võ + cs y = + V + ct10 + ct 6t y = + 2 + cr'0 11t y = + + cı'0 y = *V Tit

Chapter 2, Section 2.4, Additional Question 04 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(i)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. If n + 0, 1, then the substitution v = y-" reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. Py + 5ty – y' = 0, t>0 y = + Võ + cs y = + V + ct10 + ct 6t y = + 2 + cr'0 11t y = + + cı'0 y = *V Tit

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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The subject is differential equation
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-y-* reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. 1²y + 4ty-y²=0,t> 0 +cª +a O O O O O 1+ y = ± 1+ y = ± 5t +c8 22 9 + c +48
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