 # Ordinary Differential Equations

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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.
Solution to a 2nd order, linear homogeneous ODE with repeated roots
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.

2nd order ODE with constant coefficients: simple method of solution
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.
2nd order ODE with constant coefficients: non-standard method of solution
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,

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