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Differential equation implies bounded - OIMU 1998 Problem 6

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September 12, 2010
integrationcalculusderivativelimitreal analysisIberoAmerica Undergrad MO1998 IberoAmerica Undergrad MO

Problem Statement

Take the following differential equation: 3(3+x2)dxdt=2(1+x2)2e−t23(3+x^2)\frac{dx}{dt}=2(1+x^2)^2e^{-t^2} If x(0)≤1x(0)\leq 1, prove that there exists M>0M>0 such that ∣x(t)∣<M|x(t)|<M for all t≥0t\geq 0.
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