Subject: Re: [Maxima] Re: [Maxima] problems with solve()
From: Stavros Macrakis
Date: Mon, 26 Sep 2005 18:48:23 -0400
Here's a method for solving atan(a*x)+atan(x)+c=0.
(%i1) atan(a*x)+atan(x)+c;
(%o1) ATAN(a*x)+ATAN(x)+c
(%i2) tan(%),trigexpand;
(%o2) (-a*TAN(c)*x^2+a*x+x+TAN(c))/(-a*x^2-a*TAN(c)*x-TAN(c)*x+1)
(%i3) solve(%,x);
(%o3) [x = -(SQRT(4*a*TAN(c)^2+a^2+2*a+1)-a-1)/(2*a*TAN(c)),x =
(SQRT(4*a*TAN(c)^2+a^2+2*a+1)+a+1)/(2*a*TAN(c))]
Unfortunately, it doesn't work for the original problem, which is of
the form atan(a*x)*b+atan(x)+c=0. That is soluble in closed form only
for a few values of b.