How do you solve a 2nd order differential equation like this?
Answer:
look up undetermined coefficients. just rewrite the equation as
y"+y' = (-a/b)x should work
heck. I left my geometry book in Ms Rosenblue's class for talking to Tammy. I can look this up until next tuesday if my book still there.
This is a constant coefficient DE, so you look at the characteristic equation. That is
r^2+r+a/b=0.
Solve for r, obtain two values r1 and r2. Then exp(r1 x) and exp(r2 x) will be your solutions provided that r1 is different from r2. If they are the same, it is a little trickier but not too bad. IF r1 and r2 are complex numbers than you have to interpret exp (r1 x) and exp (r2 x) in terms of trig functions. If you need more help, just take a look at any diff eq book or web search "constant coefficient differential equations".
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