Preface; 1. Of the nature and origin of differential equations; 2. On differential equations of the first order and degree between two variables; 3. Exact differential equations of the first degree; 4. On the integrating factors of the differential equation; 5. On the general determination of the integrating factors of the equation; 6. On some remarkable equations of the first order and degree; 7. On differential equations of the first order, but not of the first degree; 8. On the singular solutions of differential equations of the first order; 9. On differential equations of an order higher than the first; 10. Equations of an order higher than the first (cont.); 11. Geometrical applications; 12. Ordinary differential equations with more than two variables; 13. Simultaneous differential equations; 14. Of partial differential equations; 15. Partial differential equations of the second order; 16. Symbolical methods; 17. Symbolical methods (cont.); 18. Solution of linear differential equations by definite integrals; Answers; Appendix; Corrections.