Differential Equations Quiz
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FOUNDATIONS & QUALITATIVE ANALYSIS
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Consider the IVP y′=ln⁡(x+5)y−3y' = \frac{\ln(x+5)}{y-3}, y(0)=1y(0)=1. The Existence and Uniqueness Theorem guarantees a unique solution exists in some neighborhood of x=0x=0. The conditions of the theorem are satisfied on any open rectangle containing the initial point (0,1)(0,1) where f(x,y)f(x,y) and ∂f∂y\frac{\partial f}{\partial y} are continuous. What is the largest open interval of xx-values, containing x0=0x_0=0, that is part of such a region of continuity?
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