Question

1. Consider the non-linear differential equation dy/dt = t/y . It was observed in Problem Set
2 that y = t is a solution to this differential equation.
(a) Verify that y = −t is also a solution.
(b) The solutions y = t and y = −t appear to cross at the point t = 0, y = 0. Why
does this not violate the uniqueness principle?
(c) By substituting into the differential equation verify that y = 2t is not a solution.

Answer 1

y=-t
imlplies t/y=-1
diffretiating both sides
\[\frac{dy}{dt}=-1\]
so you see

Answer 2

i dont really see it.