I have more equations for all the people who (don't) read this!
I love equations, especially if I can use them.
So, there are three equations for three cases of finding solutions for differential equations. This is not going to be an explanation of differential equations and how to find their solutions, so just ignore that if you don't know what they are. The important thing is that I have three new equations that I like and that I have memorized because I have been doing so many problems with them and I would like to share them with everyone.
The three equations are as follows:
I am sorry they are so small. If you click on the picture, you can see them better. I have to figure out how to get alphas and betas in a blogger post still. Anyway, the first equation is for case 1 where you find the roots of a quadratic equation and the roots turn out to be nice ordinary ones (this is just more mathematical jumble, so if you don't understand it, don't worry about it). The second equation is for case 2 where the roots turn out to be one repeated root. The third equation is for complex roots. Those are the roots that get imaginary numbers in them.
And I think these equations are so fun. They save a lot of work.