Question: 4. The solution to a linear ODE is unique and exists on R. This is however not true for general nonlinear systems. a) Show

4. The solution to a linear ODE is unique and exists on R. This is however not true for general nonlinear systems. a) Show that the solution to i = 1 + x2, x(0) = xo, does not exist on R, but only a subset of R. What is the domain of the solution? Now draw the phase portrait for this ode. What does it predict? Comment on your observations. b) Show that x = x/3, x(0) = 0 lacks a unique solution (in fact, it has infinite solutions!) i

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