Differential Equations English 2006

1. Differential Equations of the First Order and the First Degree; Definitions; Arbitrary Constants; Equations of the First Order and First Degree; Equations in which the Variables are Separable; Homogeneous Function; A Test for Homogeneity of a Function of X and Y; Homogenous Equations; Equations Reducible to a Homogeneous Form; Linear Differential Equations; Equations Reducible to Linear Form; Exact Differential Equations; Condition That an Equation of First Order and First Degree be Exact; Solution of an Exact Differential Equation; Integrating Factor; Integrating Factor by Inspection; Rules for Finding Out Integrating Factors; Change of Variables; 2. Different Equations of the First Order, but Not of the First Degree; Types of Such Equations; Equations Solvable for p ; Equations Solvable for Y; Equations Solvable for X; Clairaut's Equation; 3. Singular Solutions and Orthogonal Trajectories; Singular Solution; Determination of Singular Solution; Particular Case; Trajectories; Orthogonal Trajectory; Differential Equation of Orthogonal Trajectories; 4. Linear Differential Equations with Constant Coefficients; Definition; Theorem 1; Theorem 2; Theorem 3; Complementary Function; The Symbol D ; Auxiliary Equation having Equal Roots; Auxiliary Equation having Imaginary Roots; The Particular Integral; Shorter Methods of Finding Particular Integrals in Certain Special Cases; 5. Miscellaneous Differential Equations; Homogeneous Linear Equations; Equations Reducible to Homogeneous Linear Form; Simultaneous Linear Differential Equations with Constant Coefficients