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math.CA2025
Integration of an arbitrary linear ODE
Peter C. Gibson
The standard text book theory of ODEs lacks a general method to solve linear equations having variable coefficients, providing instead a collection of special techniques for partic…
math.CA2025
Solution of the scalar Riccati equation
Peter C. Gibson
The scalar Riccati equation is a prototypical nonlinear ODE having diverse mathematical connections. In the centuries since its initial formulation, a standard textbook theory has…