According to Wikipedia, "d'Alembert's Test" is called "ratio test" in English. Try it on series sum(1/(2^n+3^n),n=1..infinity);

> f := x -> a*x^3+b*x^2+c*x+d; f := proc (x) options operator, arrow; a*x^3+b*x^2+c*x+d end proc > locmax_conditions := {f(-1)=-2,D(f)(-1)=0}; locmax_conditions := {3*a-2*b+c = 0, -a+b-c+d = -2} > locmin_conditions := {f(4)=4, D(f)(4)=0}; locmin_conditions := {48*a+8*b+c = 0, 64*a+16*b+4*c+d = 4} > solve(locmax_conditions union locmin_conditions); {a = -12/125, b = 54/125, c = 144/125, d = -172/125} > subs(%,f(x)); -(12/125)*x^3+(54/125)*x^2+(144/125)*x-172/125

And probably the professor wanted *him* to program it, rather than using some pre-programmed "lambda" function. --- G A Edgar

> solucion[1] := {x=2,y=3}; > solucion[2] := {x=3,y=4}; > solucion[3] := {x=2,y=0}; solucion[1] := {x = 2, y = 3} solucion[2] := {x = 3, y = 4} solucion[3] := {x = 2, y = 0} > for i from 1 to 3 do > x[i] := subs(solucion[i],x); > y[i] := subs(solucion[i],y); > end do; x[1] := 2 y[1] := 3 x[2] := 3 y[2] := 4 x[3] := 2 y[3] := 0 > x[2]; 3

]]How do I display the solutions it has when it says some may have been lost? I believe it first displays all the solutions it has, then it says "some solutions may have been lost" --- G A Edgar

Re(int(1/x,x)); ln(|x|) --- G A Edgar

plot([x^2/20,sin(x),2-x], x=0..5, color=[red,black,green]); If you live in Canada (or even if you don't) you can write colour for color. --- G A Edgar

# try everything up to 1000, if no result increase the bound for N from 1 to 1000 if irem(N,21)=19 then ...... end if; end for; --- G A Edgar

Maybe it would be better to use the regular int, rather than the inert substitute Int ?? It looks like just a polynomial in t, so after integration it should be much easier to work with, even if it has giant coefficients. --- G A Edgar

N. G. De Bruijn, "The Difference-Differential Equation F'(x) = e^(alpha*x+beta)*F(x-1)." Indagationes Math. 15 (1953) 449--464. If you write F(x) = e^(-x)*f(x), your equation becomes one of his. --- G A Edgar

Must be those pirates operating off Somalia. --- G A Edgar

It is hard to tell what you mean. Maybe give an example. Perhaps you need to increase the printlevel ... are your prints inside a loop or procedure? --- G A Edgar

f := (x,t)->t-x^3; f := proc (x, t) options operator, arrow; t-x^3 end proc f(x,t)=0; t-x^3 = 0 fsolve(f(x,t)=0,x); Error, (in fsolve) t is in the equation, and is not solved for g := unapply('fsolve(f(x,t)=0,x)',t); g := proc (t) options operator, arrow; fsolve(f(x, t) = 0, x) end proc g(0.2); .5848035476 evalf(Int(g,0..1)); .7500000000

Certain definite integrals of this kind are known... int(cos(a*sin(t)),t=0..Pi/2); (1/2)*Pi*BesselJ(0, a) --- G A Edgar

You want a closed-form solution? Why do you think there is one? Even this simplified equation is not solved by Maple: > de1 := diff(y(x),x) = 1/(y(x)-sin(x)); de1 := diff(y(x), x) = 1/(y(x)-sin(x)) > dsolve(de1,y(x)); > --- G A Edgar