Let’s consider the differential equation \(y^{\,\prime }=y^{2/3}e^{x/3}\).

(a)
Does this equation have any constant solutions?

(b)
Let’s write this equation the form \(h(y)y^{\,\prime }=g(x)\).
(c)
Let’s integrate both sides with respect to \(x\).
(d)
Now let’s solve this differential equation for its general solution (including any constant solutions).
(e)
From the above, let’s determine TWO solutions to the IVP \(y^{\,\prime }=y^{2/3}e^{x/3}\) \(y(0)=0\).
(f)
Why doesn’t this contradict the Existence and Uniqueness Theorem?