I have two very difficult (for me) questions due tomorrow, and my friends who usually help when stuck are in the midst of statics and physics finals ... so if someone can help with the two I am posting, I would so appreciate it. These are due tomorrow. Happy Holidays!
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I think you might have mistyped something, since that is not a differential equation.
Edit: That makes sense.
We can find the equation's polynomial (it might be a 'characteristic polynomial' or a 'representative polynomial'; something like that)
-1/3(n^2) + n + 6 = 0
n^2 - 3n - 18
(n+3)(n-6) = 0
Now I used n on purpose, though it is more typical to use r, or some other 'neutral' variable. That's because the general solution is SUM [ ce^(nx) ], where the n's are the solutions of the polynomial.
But if e^nx is a solution, then we assume all the c's are 0 except one which is e.
The general solution for this problem is ce^6x + Ce^-3x
Thus if n=6 or n=-3, this y will solve the differential equation.
Hope this helps.
Edit: That makes sense.
We can find the equation's polynomial (it might be a 'characteristic polynomial' or a 'representative polynomial'; something like that)
-1/3(n^2) + n + 6 = 0
n^2 - 3n - 18
(n+3)(n-6) = 0
Now I used n on purpose, though it is more typical to use r, or some other 'neutral' variable. That's because the general solution is SUM [ ce^(nx) ], where the n's are the solutions of the polynomial.
But if e^nx is a solution, then we assume all the c's are 0 except one which is e.
The general solution for this problem is ce^6x + Ce^-3x
Thus if n=6 or n=-3, this y will solve the differential equation.
Hope this helps.