Consider the differential equation dx dt = f(t, x), where f and are both continuous functions for all t and x. af 𐐀x Def

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Consider the differential equation dx dt = f(t, x), where f and are both continuous functions for all t and x. af 𐐀x Define xa(t) as the solution to this differential equation with initial condition x(to) = a and define ï¿(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 2a(t*) = 2b(t*).