Let dydt2y4yy2 a What does the Existence and Uniqueness Theo

Let dy/dt=(2-y)(4-y)y²

a) What does the Existence and Uniqueness Theorem guarantee about a solution if the initial condition is y(1)=3?

b) Find and classify all of the equilibrium solutions to the ODE as nodes, sinks, or sources

c)Draw the phase line for the ODE and use it to make a qualitative sketch of the solution curves

Solution

Given that

y\'=(2-y)(4-y)y2