Ordinary differential equations

Basic definitions, solution to a differential equation, general, particular, and singular solutions, Cauchy initial problem

Differential equations with separable variables

Methods for solving ordinary differential equations with separable variables

Linear differential equations with constant coefficients

Independent solutions, Wronskian of a solution, properties of Wronskian, homogeneous and non-homogeneous problems, variation-of-constants method for finding a particular solution, special forms of right-hand-sides

Matrix functions

Methods of defining the value of a function at a square matrix

Systems of linear differential equations with constant coefficients

Homogeneous and non-homogeneous systems of linear differential equations, fundamental solution matrix, solving systems of linear differential equations with constant coefficients using the exp(xA) matrix function, variation-of-constants method