In Problems 19 and 20 verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y=ϕ(x) in each case. Use a graphing utility to obtain the graph of an explicit solution. Give an interval I of definition of each solution ϕ. dX/dt =(X-1)(1-2X); ln((2X-1)/(X-1))=t

In Problems 19 and 20 verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y=ϕ(x) in each case. Use a graphing utility to obtain the graph of an explicit solution. Give an interval I of definition of each solution ϕ. dX/dt =(X-1)(1-2X); ln((2X-1)/(X-1))=t

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.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 1CR

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Question

dX/dt =(X-1)(1-2X); ln((2X-1)/(X-1))=t

In Problems 19 and 20 verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit
solution y = 6(x) in each case. Use a graphing utility to obtain the graph of an explicit solution. Give an interval I of definition of each solution o.
( 2X – 1
In
X – 1
dX
19.
(X – 1)(1 – 2X);
= t
dt

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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