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Differential EquationsEasyNonlinear Systems & Linearization

Nonlinear Systems & Linearization · Easy problem

For the oscillator x′=y,  y′=−x3x' = y,\; y' = -x^3, the energy E=y22+x44E = \dfrac{y^2}{2} + \dfrac{x^4}{4} is conserved. A solution starts at rest at x=2x = 2, i.e. at (2,0)(2, 0). What is the largest speed ∣y∣|y| it ever reaches?