(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Verify that the indicated funciton is a solution of the given Differential Equation. c_{1}and c_{2}denote constants where appropriate.

[tex]\frac { dX }{ dt } =(2-x)(1-x);\quad \quad \ln { \frac { 2-x }{ 1-x } } =t[/tex]

3. The attempt at a solution

I'm not quite sure how to really start this problem. If I'm reading the question right, the differential equation is

[tex]\frac { dX }{ dt } =(2-x)(1-x)[/tex]

and that the solution I'm checking is

[tex]\ln { \frac { 2-x }{ 1-x } } =t[/tex]

I was thinking of perhaps integrating

[tex]\frac { dX }{ dt } =(2-x)(1-x)[/tex]

then maybe plug in the the given value of t?

I've read through the section and looked at my notes from class, but I can't seem to fully understand what I should be doing in this problem. The solution in the back of the book says

[tex]\frac { d }{ dt } \ln { \frac { 2-X }{ 1-X } } =1,\quad \left[ \frac { -1 }{ 2-X } +\frac { 1 }{ 1-X } \right] \frac { dX }{ dt } =1[/tex]

Simplifies to

[tex]\frac { dX }{ dt } =(2-X)(1-X)[/tex]

...Notentirelysure what it necessarily means by that though. Any help would be GREATLY appreciated.

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# Differential Equations - Verifying a solution of a given DE

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