I am working on Section 13.1 from Advanced Engineering Mathematics(3rd Edition)

Question

I am working on Section 13.1 from Advanced Engineering Mathematics(3rd Edition) by Zill and I am getting stuck on Part 3 of everyquestion. I am specifically on question 4 right now and I don'tunderstand how they solve the linear homogeneous differentialequations. They go from X' + (/x)X = 0 to a solution. I don'tremember if there are equations to solve these equations or how tosolve them. (Not just this one but these equations in general) Anyhelp would be greatly appreciated! Thanks!

I know these are first order but I don't know how to solve secondorder ordinary differential equations either. (The three cases asin question 12 from this section)

Explanation / Answer

A few guidelines: 1) If you're working with polynomials, you can usuallymanipulate the coefficient and add to the exponent to workbackwards. 2) If you're working with trig functions, remember that theymodulate. 3) If you're working with e-functions (e.g. e^x, etc.) youusually won't have to do anything.
It's necessary to have a good background in general solutionsto homogeneous equations in order to solve boundary-value problemslater, so make sure you can come up with the y, y', and y''easily.
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