3 ms·
Can anyone explain why it takes so long to find the equation differentially? I understand that is subjective, but the 'constants' are only constant from y''' to
by tkahn6 17y ago
Can anyone explain why it takes so long to find the equation differentially? I understand that is subjective, but the 'constants' are only constant from y''' to y''. From y'' to y' the 'constant' is linear (meaning you have to solve for change in y' - y) and the 'constant' is quadratic from y' to y.
Basically you can't just integrate each DE and solve for a constant C by finding the value of the lower order DE where x=1 and finding the difference. Why not?
I'm in Calc BC in high school so this could be a stupid question.
- shrughes 17y agoHuh? What DE?
- jacobolus 17y agoThis is just a sequence being modeled by a polynomial. The point of a "difference table" is that when you take enough levels of differences (if you like you can think of these as analogous in some way to derivatives, insofar as each step of grabbing differences reduces the order of a polynomial sequence by one power, but it's not really necessary), you eventually get down to a constant, from which you can work backwards to figure out what the patterns in higher-up differences are.
- tkahn6 17y agoI'm aware difference tables can be used to find the final term in the sequence - it's what I did to find the answer. I was using differential equations to find the equation that describes the sequence and I was wondering why the constant that you get when you integrate a function isn't actually a constant after the second integration.