Related Topics:

More Lessons for Engineering Mathematics

Math Worksheets

A series of free Engineering Mathematics video lessons.

Homogeneous first order ordinary differential equation

I discuss and solve a "homogeneous" first order ordinary differential equation. The method involves a substitution. Such an example is seen in 1st and 2nd year university mathematics.

I discuss and solve a 2nd order ordinary differential equation that is linear, homogeneous and has constant coefficients. In particular, I solve y'' - 4y' + 4y = 0. The solution method involves reducing the analysis to the roots of of a quadratic (the characteristic equation). Such an example is seen in 1st and 2nd year university mathematics.

I give a simple and direct method to solve the ODE y'' + y' - 6y = 0. The method involves analysis of the associated characteristic equation. This type of problem is seen in 1st-year university mathematics.

I present a direct and non-standard method of solution to the 2nd order homogeneous ODE with constant coefficients, namely y'' - 4y' + 4y = 0. I do not explicitly use the characteristic equation, rather I reduce the problem to the analysis of a first order ODE. Such a method shows exactly why the solution features exponential functions and illustrates where they come from,

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

data-ad-region="y21">