3. Consider the IVP:
dy =ty^1/3; y(0)=0,t≥0. dt
Both y(t) = 0, (the equilibrium solution) and y(t) =
?(1/3t^2?)^3/2 are solutions to this IVP.
(a) Show that the trivial solution satisfies the IVP by first
verifying that it satisfies the initial condition and then
verifying that it satisfies the differential equation.
(b) Show that the other solution satisfies the IVP again by
first verifying it satisfies the initial condition and then
verifying that it satisfies the differential equation.
(c) Explain...
Consider the differential equation dy/dt = 2?square
root(absolute value of y) with initial condition y(t0)=y0
• For what values of y0 does the Existence Theorem apply?
• For what values of y0 does the Uniqueness theorem apply?
• Verify that y1(t) = 0 solves the initial value problem with y0 =
0
• Verify that y2(t) = t2 solves the initial value problem with y0 =
0
• Does this violate the theorems from this section 1.5? Why or why...