@Carl Love 

I have been stuck in here for days, so I am really grateful for that you helped me out of it and taught me a new method I didn't know before to draw a space curve based on DEs. Thank you, man.

@Carl Love 

X := 2*cos(V);
Y := 2*sin(V);
Z := U;
GrPlane := plot3d([X, Y, Z], U = 0 .. 10, V = 0 .. 2*Pi);
E := simplify((diff(X, U))^2+(diff(Y, U))^2+(diff(Z, U))^2);
G := simplify((diff(X, V))^2+(diff(Y, V))^2+(diff(Z, V))^2);
pdE := diff(log(E), V);
pdG := diff(log(G), U);
U := u(s);
V := v(s);
eqn1 := simplify(diff(U, s) = cos(theta(s))/sqrt(E));
eqn2 := simplify(diff(V, s) = sin(theta(s))/sqrt(G));
eqn3 := simplify(diff(theta(s), s) = pdE*cos(theta(s))/(2*sqrt(G))-pdG*sin(theta(s))/(2*sqrt(E)));
with(DEtools); with(plots); GrGline := DEplot3d({eqn1, eqn2, eqn3}, {theta(s), u(s), v(s)}, s = 0 .. 5, [[u(0) = 1, v(0) = Pi, theta(0) = (1/4)*Pi]], scene = [X, Y, Z]);

display(GrGline, GrPlane)