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4962Multiplicity Diagnostic 19Why can a boundary value problem have multiple solutions even when the corresponding initial-value problem is unique for each chosen slope?数学困难essay未尝试面试订阅4963Neumann Compatibility Diagnostic 20Why does a pure Neumann problem for y'' = f sometimes need a compatibility condition before any solution can exist?数学困难essay未尝试面试订阅4964Finite-Difference Diagnostic 21Why can a finite-difference solve be more numerically stable than naive shooting for a stiff BVP?数学困难essay未尝试面试订阅5858Integrating Factor with Variable CoefficientSolve the first-order linear ODE x'(t)+\dfrac x(t) t =t for t>0 with x(1)=2, and evaluate x(2).数学中等derivation未尝试面试订阅5859Separable Nonlinear ODE and Blow-UpSolve the separable ODE y'(x)=x\,y(x) 2 with y(0)=1. At what value of x>0 does the solution blow up?数学中等derivation未尝试面试订阅5860Overdamped Second-Order ODE with Distinct Real RootsSolve y''-5y'+6y=0 with y(0)=1 and y'(0)=0.数学中等derivation未尝试面试订阅