The equation P(x)y” + Q(x)y’ + R(x)y= 0 is said to be exact if it can be written in the form [P(x)y’]’ + [f(x)y]’=0, where f(x) is to be determined in terms of P, Q, and R. The latter equation can be integrated once immediately, resulting in a first order linear eq for y that can be solved. By equating the coefficients for the preceding equations and then eliminating f(x), show that a necessary condition for exactness is P”(x) – Q’(x) + R(x) =0 . It can be shown that this is also a sufficient condition.
You don’t actually have to do this problem, but it’s supposed to help with the one I’m supposed to do.
1) x2y” + xy’ – y = 0, x>0.
How would you do this problem… or solve any exact equation
2006-10-12
12:13:39
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2 answers
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asked by
Anacapa
2
in
Mathematics