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Extension: Integrating Factors for Differential Equations

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Explanations 1

A first-order linear differential equation is an equation that can be put into the following form: dydx+P(x)y=Q(x)\frac{dy}{dx} + P(x)y = Q(x)dxdy+P(x)y=Q(x) As an example, con…
By Sujay Kazi

Problems 2

(HMMT February 2002, Calculus Round, #9) Suppose fff is a real differentiable function such that f(x)+f′(x)≤1f(x) + f'(x) \le 1f(x)+f′(x)≤1 for all xxx, and f(0)=0f(0) = 0f(0)=0…
Let fff be a differentiable real function such that f(−1)=f(0)=f(1)=0f(-1) = f(0) = f(1) = 0f(−1)=f(0)=f(1)=0. What is the smallest possible number of distinct real zeros the fu…