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Differential Equations - Notes

Internet Explorer 10 & 11 Users : If you have been using Internet Explorer 10 or 11 to view the site (or did at one point anyway) then you know that the equations were not properly placed on the pages unless you put IE into "Compatibility Mode". I believe that I have partially figured out a way around that and have implimented the "fix" in the Algebra notes (not the practice/assignment problems yet). It's not perfect as some equations that are "inline" (i.e. equations that are in sentences as opposed to those on lines by themselves) are now shifted upwards or downwards slightly but it is better than it was.

If you wish to test this out please make sure the IE is not in Compatibility Mode and give it a test run in the Algebra notes. If you run into any problems please let me know. If things go well over the next week or two then I'll push the fix the full site. I'll also continue to see if I can get the inline equations to display properly.
 First Order DE's Previous Chapter Next Chapter Laplace Transforms Euler's Method Previous Section Next Section Basic Concepts

## Second Order Differential Equations

In the previous chapter we looked at first order differential equations.  In this chapter we will move on to second order differential equations.  Just as we did in the last chapter we will look at some special cases of second order differential equations that we can solve.  Unlike the previous chapter however, we are going to have to be even more restrictive as to the kinds of differential equations that we’ll look at.  This will be required in order for us to actually be able to solve them.

Here is a list of topics that will be covered in this chapter.

Basic Concepts  Some of the basic concepts and ideas that are involved in solving second order differential equations.

Real Roots  Solving differential equations whose characteristic equation has real roots.

Complex Roots  Solving differential equations whose characteristic equation complex real roots.

Repeated Roots  Solving differential equations whose characteristic equation has repeated roots.

Reduction of Order  A brief look at the topic of reduction of order.  This will be one of the few times in this chapter that non-constant coefficient differential equation will be looked at.

Fundamental Sets of Solutions  A look at some of the theory behind the solution to second order differential equations, including looks at the Wronskian and fundamental sets of solutions.

More on the Wronskian  An application of the Wronskian and an alternate method for finding it.

Nonhomogeneous Differential Equations  A quick look into how to solve nonhomogeneous differential equations in general.

Undetermined Coefficients  The first method for solving nonhomogeneous differential equations that we’ll be looking at in this section.

Variation of Parameters  Another method for solving nonhomogeneous differential equations.

Mechanical Vibrations  An application of second order differential equations.  This section focuses on mechanical vibrations, yet a simple change of notation can move this into almost any other engineering field.

 Euler's Method Previous Section Next Section Basic Concepts First Order DE's Previous Chapter Next Chapter Laplace Transforms

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