Question 5 Consider the differential equation dx dt = f(t, x), = where f and of are both continuous functions for all t

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Question 5 Consider The Differential Equation Dx Dt F T X Where F And Of Are Both Continuous Functions For All T 1 (65.08 KiB) Viewed 42 times

Question 5 Consider the differential equation dx dt = f(t, x), = where f and of are both continuous functions for all t and î. Define xa(t) as the solution to this differential equation with initial condition x(to) = a and define x (t) as the solution to this differential equation with initial condition x(to) = b, where to, a and b are constants. Prove that if a ‡ b then the graphs of xa and never cross. That is, prove that there is no time t* such that xa (t*) = x₂(t*).