Added by astrobookcat1 on May 06, 2002 at 19:50:46:
The equation should have the form y" +py' +qy = 0, so plug in powers of m for the primes and to convert it to a characteristic equation of m^2 +pm+ q, and solve it like a quadratic. If you get two real roots, the equation will take the form y = Ce^(m1x) + De^(m2x) where m1 and m2 are the roots and C and D are arbitrary constants you'll have to find with initial conditions. If there is only one repeated real root, the equation will be y = Ce^(mx) +Dxe^(mx). And finally, if you get imaginary roots of the form aħbi, your general solution will be y = e^(ax)*[Ccos(bx) +Dsin(bx)].