What's the difference between a 2nd order DE equation and Euler Cauchy equation?

Question

anonymous · Answer

Looking a question I was given, from the looks of things I solve the same the way.

anonymous · Answer

That's a 2nd order DE? http://i.imgur.com/EQFtW.jpg

anonymous · Answer

usually second order will require functions were you take the derivative more than one that you will end up with the original. 

This can be cos sin and e^x functions.

anonymous · Answer

ok so, but I can solve them the exact same way

anonymous · Answer

I mean all I did for that equation was get the characteristic equation and get the roots from a quadratic formula

anonymous · Answer

Euler Cauchy equation is a second order differential equation. If you have been solving Euler Cauchy equation a certain way then use the same method.

anonymous · Answer

I see, I was just wondering because this was from a exam paper from last year, before the question in the link there's 2nd order DE question.

I was wondering why the both on the same paper considering I solve them the same way...

anonymous · Answer

You can tell that it's a second order because of the notation. d^2x/dt^2 second order
dx/dt  is first order.

anonymous · Answer

I know, but when first saw the equation I posted, I noticed it was in 2nd order DE form, it confused me they fact called a Euler Cuachy equation. I thought it was something completely different.