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Origin of Differential Equations.Solutions of Differential Equations.Equations of First Order and First Degree.Variables Separable; Exact Equations.Linear Equations.Geometric Applications.Physical Applications.Equations of First Order and Higher Degree.Singular Solutions.Extraneous Loci.Applications of First Order and Higher Degree Equations.Linear Equations of Order n.Homogeneous Linear Equations with Constant Coefficients.Linear Equations with Constant Coefficients.Short Methods.Linear Equations with Variable Coeffiecients--The Cauchy and Legendre Linear Equations.Linear Equations with Variable Coefficient--Equations of the Second Order.Linear Equations with Variable Coefficients--Miscellaneous Types.Applications of Linear Equations.Simultaneous Linear Equations.Total Differential Equations.Applications.Numerical Approximations.Integration in Series.The Legendre, Bessel, and Gauss Equations.Partial Differential Equations.Linear Partial Differential Equations of Order One.Non-Linear Partial of Order One.Homogeneous Partial of Higher Order with Constant Coefficients.Non-Homogeneous Linear Equations with Constant Coefficients.Partial Differential Equations of Order Two with Variable Coefficients.