Given a scalar autonomous differential equation $$u'(t)=\gamma u(t)^n, \,\,\,\,t \geq 0$$ where $\gamma \in \mathbb R \,$, $n \in \mathbb N$. How can I check wether the null solution is (asymptotic/exponential) or attractive?
How to check wether a solution is asymptotic, exponential or attractive.
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real-analysis
ordinary-differential-equations
1 Answers
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Thew stability of the null solution will depend on the sign of $\gamma$. You can see this solving the equation explicitely.