No, you are not missing something obvious; a workaround:
(%i12) load(to_poly_solver)$
(%i13) sol : %solve(y=x+h*C*sqrt((y+x)/2),y);
(%o13) %union(%if((-%pi/2<parg(sqrt(2)*h*C-sqrt(2)*sqrt(h^2*C^2+16*x))) %and (parg(sqrt(2)*h*C-sqrt(2)*sqrt(h^2*C^2+16*x))<=%pi/2), [y=-(h*C*sqrt(h^2*C^2+16*x)-h^2*C^2-4*x)/4],%union()),%if((-%pi/2<parg(sqrt(2)*sqrt(h^2*C^2+16*x)+sqrt(2)*h*C)) %and (parg(sqrt(2)*sqrt(h^2*C^2+16*x)+sqrt(2)*h*C)<=%pi/2),[y=(h*C*sqrt(h^2*C^2+16*x)+h^2*C^2+4*x)/4],%union()))
(%i14) subst([h=1,C=1,x=-1/16],sol);
(%o14) %union([y=3/16])
(%i15) subst([h=1,C=1,x=-1/16 + 4],sol);
(%o15) %union([y=99/16])
(%i16) subst([h=1,C=1,x=-1/16 - 4],sol);
(%o16) %union([y=(8*%i-61/4)/4],[y=-(8*%i+61/4)/4])
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
Why can't Maxima find an explicit solution for y?
Am I missing something obvious?
(%i1) kill(all)$
????? display2d:false$
(%i2) solve(y=x+h*C*sqrt((y+x)/2),y);
(%o2) [y = (h*sqrt(y+x)*C+sqrt(2)*x)/sqrt(2)]
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