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# differential equations watch

1. ok i've tried searching all over google for diff.eq, but they all come up in the form y"+y'+y or y'+y, but nothing like y"+y' or y"+y (hope this isn't too confusing! )

do these kind of diff.eq have a name so i can search for it on google more specifically? or can anyone tell me what the hell the teacher's doing?! (just small parts of it would help majorly!!) thanks!
2. Basic differential equations will come up in the form ay'' + by' + cy = f(x), but you're perfectly welcome to set b = 0 or c = 0 in there to get the equations you were talking about. The one your teacher has solved for you is a different one entirely - the coefficients are no longer constant (i.e. they're things like x and x^2, which are obviously changing as x changes), which makes things quite difficult. Your teacher has obviously seen this type of equation before, because (s)he knew that making the substitution x = e^t was going to be a helpful thing to do. The equation is now in terms of y and t rather than y and x, and turns out to be much nicer. (Exponential functions like e^ax are frequently very useful, because they are eigenfunctions of the differential equation operator - that is, their derivatives are constant multiples of themselves.)

This website goes through loads of different types of differential equations - it's not very 'basic', but it does show you how to solve them.

If you need any more help with specific lines of that solution, let me know - but there's not really much I can do if you don't tell me where you're struggling.

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Updated: August 7, 2009
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