# 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.

Single-variable Calculus

Multi-variable Calculus

Engineering Mathematics

Linear Algebra and its Applications For differential equations, a book (in Persian) by Dara Moazzami (pictures) has been also always very useful.