Theory of Differential Equations : Ordinary Equations, Not Linear (Paperback)

1. Introductory; 2. Cauchy's theorem on the existence of regular integrals of a system of equations; 3. Classes of non-ordinary points connected with the form of the equation of the first order and first degree in the derivative; 4. Influence, upon the integral, of an accidental singularity of the first kind possessed by the equation; 5. Reduction of the differential equation to final typical forms, valid in the vicinity of an accidental singularity of the second kind; 6. The character of the integrals possessed by the respective reduced forms of the original equation in the vicinity of the accidental singularity of the second kind; 7. Effect, upon the integral, of essential singularities of the equation; 8. Branch-points of an equation of the first order and any degree, as determined by the equation: singular and particular solutions; 9. Differential equations of the first order having their integrals free from parametric branch-points; 10. Equations of first order with uniform integrals, and with algebraical integrals.