Answered: (出) 2 d²y dy = 0, dx dy dx? dx

Math

Calculus

(出) 2 d²y dy = 0, dx dy dx? dx

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 22CR

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Question

Consider the non-linear differential equation (provided) with boundary condition y(0) = 0.

Show that this equation can be converted into a first-order differential equation using p(x) = dy/dx. Explicitly solve the differential equation to find p(x) = Be^−x/(1 − Be^−x), where B is a constant, and hence find the general solution y(x) in terms of one undefined constant.