## Related questions with answers

Question

(i) sketch the differential equation in the $y-y^{\prime}$ plane by hand. (ii) Draw the phase line diagram, clearly stating the location and stability of the equilibria. (iii) State the long-term behavior for all initial conditions. (iv) Assuming y = y(x), sketch the corresponding graph in the traditional x-y plane. $y^{\prime}=-y^{2}$

Solution

VerifiedStep 1

1 of 4We have a parabola whose root is $0$ of multiplicity 2 in the $y-y'$ plane.

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