Re: differential equation of second order

In article <KMWWf.181$hx4.71@xxxxxxxxxxxxxxxxxxx>,
db <danteb@xxxxxxxxxxx> wrote:


someone can tell me if the differential equation of second order
y''(x)+ay'(x)+b/y(x)=0 as an exact resolution?

Maple gives the solution as

y(x) = RootOf(

_Z
/
| 1
-exp(a x) + | -------------------------- d_f a + _C2 a)/
| 1/2
/ (-2 b ln(_f) + 2 _C1 b)


exp(a x)

i.e. if F(t) = int 1/sqrt(2 C_1 b - 2 b ln(t)) dt,
z(x) = y(x) exp(a x) satisfies F(z(x)) + C_2 = exp(a x)/a
where C_1 and C_2 are constants.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.