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Unformatted text preview: P < 1 leads to extinction of the population. 2 2. Explain why the solution to x = ( t 2 + x 2 )( x 34 x ) with x (1) = 1 will never satisfy x ( t ) > 2. Solution. This equation has the equilibrium solutions x ≡ 0, x ≡ 2 and x ≡ 2. The solution with x (1) = 1 is below the equilibrium solution x ≡ 2 when t = 1, and this equation has f ( t,x ) and ∂f ∂x ( t,x ) continuous because they are both polynomials. So the uniqueness theorem says that x ( t ) can never cross the x ≡ 2 equilibrium solution, and must remain less than 2....
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This note was uploaded on 05/01/2008 for the course MATH 33B taught by Professor Staff during the Spring '07 term at UCLA.
 Spring '07
 staff
 Differential Equations, Equations

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