Differential equation and explicit solution

Reference no: EM13119945

The problem is:

dx/dt = (x-1)(1-2x); ln {2x-1/x-1} = t

To solve this problem I must, first, verify that the indicated expression is an implicit solution of the given first-order differential equation then find at least one explicit solution. The last element of the solution is to use a graphing utility to obtain the graph of an explicit solution and give an interval of definition.

I have been working on this problem for quite a while and have been unable to come up with the solution given in the book. This solution is:

X = e^t - 1 / e^t-2 defined on (-infinity, ln2) or on (ln2, infinity)

Please supply me with a detailed answer to this problem so that I will be able to use the principles to solve more of the same type problem.

Reference no: EM13119945

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