Consider the following code:
DSolveValue[{\[DifferentialD]r[\[Theta]]/\[DifferentialD]\[Theta] == (
r[\[Theta]] \[Theta] + r[\[Theta]])/(
r [\[Theta]] \[Theta] + \[Theta]), r[1] == E},
r[\[Theta]], \[Theta]]
by hand I can arrive to
r[th] + Log[r[th]] = th + Log[th] + E
But not using DSolver neither DSolveValue,
and finally I do not get the way to plot , neither r[th] neither the vectorial ploting of field
thanks for advice and sorry if made mistakes in use of this facility
(1) It would help to format the code so it was more easily read and able to be copied into Mathematica. (2) It looks like you might be using \[DifferentialD] instead of either of the derivative operators D[r[th], th] or r'[th] to write your differential equation. The differential cannot be used to set up a differential equation. (It can be used to set up a simple Integrate[], but I usually don’t in case I want to add options, unless the integral is just for show & readability.)
msol = DSolve[{y’[x] == (x y[x] + y[x])/(x y[x] + x), y[1] == E},
y[x], x]
Maybe this is better? anyway it returns as wrong, and a solution that is different from the hand done solution…
Your manual solution, if carried further, yields
Solve[r[th] + Log[r[th]] == th + Log[th] + E, r[th]]
(* {{r[th] -> ProductLog[E^(E + th) th]}} *)
which is equivalent to the DSolve solution.
You can also verify the DSolve solution with
{y'[x] == (x y[x] + y[x])/(x y[x] + x), y[1] == E} /. msol // FullSimplify // N[#, 80] &
(For some reason Mathematica does not simplify ProductLog[E^(1 + E)], so I verified it numerically out to 80 digits – an arbitrary choice, but hopefully convincing.)
msol = DSolve[{y’[x] == (x y[x] + y[x])/(x y[x] + x), y[1] == E},
y[x], x]
Maybe this is better? anyway it returns as wrong, and a solution that is different from the hand done solution…
Yessss really it’s now all clear, I must improove a lot to do work like you! Thanks and I will try to post questions in this format in further opportunities.
I can not plot this but this happens everytime I arrive to implicit functions, I look for examples like ellipses or other implicits but sonething I made bad when change to other functions…
Welcome to Wolfram Community! Please make sure you know the rules and how to format your code properly, which you can find here: https://wolfr.am/READ-1ST If you do not format code, it may become corrupted and useless to other members. Please EDIT your posts and make sure code blocks start on a new paragraph and look framed and colored like this.
int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]
