Example: Find all solutions to
Solution: First, we look for the constant solutions, that is, we look for the roots of
This equation does not have real roots. Therefore, we do not have constant solutions.
The next step will be to look for the non-constant solutions. We proceed by separating the two variables to get
Then we integrate
Therefore, we have
It is not easy to obtain y as a function of t, meaning finding y in an explicit form.
Finally, because there are no constant solutions, all the solutions are given by the implicit equation
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Author: Mohamed Amine Khamsi