Thread: Two (probably stupidly simple) differential equations questions

Hello!

I never thought that there would be a math forum that would be this busy! Bookmarked.

Ok... enough with the sugar. I have finished almost all of my homework sheet, but I am having problems with a couple questions. My text (First course in DE, by Zill) is not helping me at all, and neither is the almighty google.

The first is asking me to find a differential equation that is satisfied by the function

I'm guessing it has to do with superposition, but I only know how to use that to get a solution from a DE, not vice versa!

Next up, I have a question asking me to find the intervals where these DEs have a unique solution:

a)
and
b)

EVERY question I've seen for finding intervals with a unique solution atleast has initial values.

I have been , and of course, the math help centre at my school only has a DE assistant when I am at work, so any help you guys give me would be frickin awesome.

Thanks!

These are not at all stupid questions!...

First answer: the general solution of the DE is...

(1)

... and that means that is a second order linear DE with constant coefficients and its 'characteristic equation' has solution with molteplicity two, i.e. is...

(2)

The corresponding DE is...

(3)

Second answer: the interval in which a linear second order DE has one and only one solution for any 'initial condition' is the inteval in which the 'coefficient' of the term doesn't vanish, i.e. . In a) is , in b) is , so that...

Kind regards

Thanks alot! That helped a lot. I can't believe how easy the second question was. It was worth as many marks as a question that took 5 times as long to do, so that is why I got tripped up by it.



+1 Thanks!