What are the most famous qualitative methods to study and analyse a differential equation?

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I need to study the Duffing-van der Pol equation $$ \ddot x - x + x^3 = \varepsilon (p_1 + p_2 x - x^2) \dot x $$ using a few qualitative methods but the problem is that I don't know any, so can you recommend some or help by pointing me to the place in which I should look? thank you in advance!