Find all solutions to the differential equation dy dt = 1 − y 2

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01-02-2018
Mathematics

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Find all solutions to the differential equation dy dt = 1 − y 2

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evgeniylevi evgeniylevi · Answer 1 · 2018-02-02T14:04:49+01:00

evgeniylevi evgeniylevi

02-02-2018

Try this:
[tex] \frac{dy}{dt}=1-y^2; \ =\ \textgreater \ \ \frac{dy}{y^2-1}=-dt; \ =\ \textgreater \ \ ln| \frac{y-1}{y+1}|=-2t+C.[/tex]
If it is possible, modify result to form more compact.

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