## 584 Reputation

7 years, 218 days

## implicit plot a complex function...

Maple

i have a function which contains Ln and arctan fanctions in which the output function is complex.
how can i implicitplot this complex function? tnx for the help

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 (1)
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 (2)
 > P:=subs(y(w)=Y,eval(lhs(Ans[1, 1]), [_C1 = 0, m = 1]))
 (3)
 > implicitplot(P,w=-10..0,Y=0..10)
 > evalf((eval(P,[w=1,Y=1])))
 (4)
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## solve a system of integral equations...

Maple

how i can solve a system of integral equations? thanks for the help.

 (1)

 (2)

## a problem with integration...

Maple

Hi dear maple team. i have a question on integration and i need a "real" and "finite" solution with any assumption or options. thanks for the help.

 > restart
 > f := ((1 - a)^2 + a^2*((1 - exp(-y))*(1 - exp(-x)) - 2 + exp(-x) + exp(-y)) + a*(2 - exp(-x) - exp(-y) + (1 - exp(-y))*(1 - exp(-x))))/(1 - a*exp(-x)*exp(-y))^3;
 (1)
 > a := 0.3;f
 (2)
 > s := 2*evalf(int((int(f*exp(-x)*exp(-y), x = 0 .. y + t,AllSolutions)), y = 0 .. infinity,AllSolutions)) assuming real ;
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## solving system of odes...

Maple

I have 4 ode equations. i just want to know can i use any option or simplification to have a analytical solution or NOT? Thanks in Advance

 > restart:
 > ode1 := -2*diff(lambda(t),t)*y1(t) - lambda(t)*diff((y1)(t),t)-0*diff(eta(t),t) - diff((y1)(t),t\$3) + diff((y1)(t),t)*(y1(t)^2 + y2(t)^2) +4*y1(t)*sqrt(y1(t)^2 + y2(t)^2)*diff(sqrt(y1(t)^2 + y2(t)^2),t)+diff((y1)(t),t)/r^2 + y1(t)^2*diff(y1(t),t) + y1(t)*y2(t)*diff(y2(t),t) - 2*diff(y1(t),t)/r^2 ;
 >
 (1)
 > ode2 := diff((lambda)(t),t\$2) + lambda(t)*(y1(t)^2 + y2(t)^2) - 2*y1(t)*diff((y1)(t),t\$2) - y1(t)^2*(y1(t)^2 + y2(t)^2) - y1(t)^2/r^2 - diff((y1)(t),t)^2 - 2*diff(sqrt(y1(t)^2 + y2(t)^2),t)^2 - 2*sqrt(y1(t)^2 + y2(t)^2)*diff(sqrt(y1(t)^2 + y2(t)^2),t\$2) - diff((y2)(t),t)^2 - 2*y2(t)*diff((y2)(t),t\$2) - y2(t)^2*(y1(t)^2 + y2(t)^2)
 (2)
 > ode3 := 2*diff((lambda)(t),t)*y2(t) + lambda(t)*diff((y2)(t),t) - y1(t)*y2(t)*diff((y1)(t),t) - 4*y2(t)*sqrt(y1(t)^2 + y2(t)^2)*diff((sqrt(y1(t)^2 + y2(t)^2)),t) - y2(t)^2*diff((y2)(t),t) - (y1(t)^2 + y2(t)^2)*diff((y2)(t),t) - diff((y2)(t),t\$3) ;
 (3)
 > ode4 := lambda(t)*y1(t)/r + mu(t)*r - diff((y1)(t),t\$2)/r -1/r*y1(t)*(y1(t)^2 + y2(t)^2) - y1(t)/r^3-2/r*diff(y1(t),t\$2)
 (4)
 > sys := [ode1, ode2, ode3, ode4]:
 > dsolve(sys,[y1(t),y2(t),lambda(t),mu(t)],'implicit')