TeachingDifferential equations – Ordinary differential equations
Definition A differential equation is an equation involving an unknown function and one or more of its derivatives. The order of the highest derivative involved is called the order of the differential equation.
Classification:
- An ordinary differential equation is about a function of one variable and its ordinary derivatives.
- A partial differential equation is about a function of several variables and its partial derivatives.
Furthermore one can distinguish between linear differential equations and nonlinear differential equations.
Goal: To find the (general) solution, the set of all solutions of the differential equation.
First-order differential equations
First-order differential equations were already treated at calculus. Among other things we have dealt with direction fields, which could be used to find information about the solutions without solving the differential equation. Furthermore, separable differential equations and linear differential equations were discussed. Also some applications in general and mixing problems in particular were dealt with.
Second-order differential equations
Second-order linear differential equations with constant coefficients were also discussed at calculus. For nonhomogeneous linear differential equations we have seen the method of undetermined coefficients there. Furthermore, some applications were treated. Here we go somewhat deeper into the theory, we will discuss the special case of Euler equations, the method of reduction of order and the method of variation of parameters.
Last modified on April 19, 2021
