**Ordinary Differential Equations**

**In mathematics, a differential equation is an equation that relates one or more functions and their derivatives.**

**In the course on ordinary differential equations, we usually deal with the following topics:**

**Separable equations****First-order linear differential equations****Bernoulli differential equations****Exact differential equations and test for exactness****Homogeneous functions and equations****Riccati, Clairaut's, and Lagrange's equations****Orthogonal trajectories****The general form of a second-order linear differential equation****Second-order linear homogeneous differential equations with constant coefficients (real, complex, and repeated roots)****Reduction of order****Linear independence and Wronskian****Nonhomogeneous linear second-order differential equations****Undetermined coefficients and variation of parameters****Higher-order differential equations****Cauchy-Euler differential equations of order****n****Power series solutions of differential equations****Regular singular points****The generalized power series method in solving differential equations****Definition of integral transforms****Definition of Laplace transform****A short table of Laplace and inverse Laplace transforms****Step functions and their Laplace transforms****Computation of Laplace transform of a function's derivative and antiderivative****Differentiation and integration of Laplace transforms****Dirac delta function****Convolution integral****Completion of the table of Laplace transforms****Systems of differential equations****Real, complex, and repeated eigenvalues and their applications in solving systems of differential equations****Nonhomogeneous systems of differential equations**

For more details, refer to the following book:

Boyce, W. E., DiPrima, R. C., & Meade, D. B. (2017). Elementary differential equations. John Wiley & Sons.

For differential equations, a book (in Persian) by **Dara Moazzami** (pictures) has been also always very useful.