- #1

oddjobmj

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## Homework Statement

Verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y=∅(x) in each case.

## Homework Equations

[itex]\frac{dX}{dt}[/itex]=(X-1)(1-2X); ln([itex]\frac{2X-1}{X-1}[/itex])=t

## The Attempt at a Solution

I know I need to solve the 't=' portion for X and here it is:

ln([itex]\frac{2X-1}{X-1}[/itex])=t =>

[itex]\frac{e^t-1}{e^t-2}[/itex]=X

In -explicit- cases I would differentiate X to find X' and replace the original X' from the given differential equation to see if it works out to 0.

I don't know how to go about proving it in the implicit case and everything I'm finding when I google is how to do implicit differentiation from a calc 2-3 perspective.

Thank you