Automated ODE Example Generator

Welcome to the automated ODE example problem generator!

If you want solved examples of second order constant coefficient ODE's (Ordinary Differential Equations), look no further. This page has (quite literally) an infinite number of worked examples!

Some explanation follows. Or, just dive right in and click the button below!

Now for the explanations

What is an ODE? The acronym ODE stands for Ordinary Differential Equation. An ODE is an equation for an unknown function, involving various derivatives of the function.

What kinds of ODE examples are generated here? This page generates examples of Second Order, Linear, Constant Coefficient ODEs. That is, all the examples generated are of the form

a y'' + b y' + c y = f(x),

where a, b and c are constants, y is an unknown function of x, and f will be either a sine or cosine function, an exponential, or a polynomial, or a combination of these. Each ODE is accompanied by some initial values of y and y'.

What can I expect when I click the button? The generator will generate and display an ODE. If you want, you can then try to solve it. When you have solved it (or anytime), you can display the solution with a single click. If you got it right, congratulations! Otherwise, check your working, or you can see the full details of the solution method by clicking another link. When you are ready for another example, just click the "generate another example" button.

Ready to try? Then Click the button already!!