Group Abstract Group Abstract

Message Boards Message Boards

0
|
56 Views
|
6 Replies
|
0 Total Likes
View groups...
Share
Share this post:

Separating variables *a* and *b* in a transcendental equation

Wen Dao
Posted 1 day ago 
eq1 = 2 (a + b) == E^(2 a) + 2 Log[b] + 1

How to transform eq1 into the form of eq2:

eq2 = E^(2 a) - 2 a + 1 == 2 b - 2 Log[b]

The transformation rule is to move terms containing the same variable to the same side of the equation. Specifically for this problem, terms with the letter 'a' should be moved to one side, while terms with 'b' should be moved to the other side.
POSTED BY: Wen Dao
6 Replies
Sort By:

Here is a way using SubtractSides:

eq1 = 2 (a + b) == E^(2 a) + 2 Log[b] + 1 // Expand
SubtractSides[eq1,
 Select[eq1[[1]], FreeQ[a]] +
  Select[eq1[[2]], FreeQ[b]]]
POSTED BY: Gianluca Gorni
Wen Dao
Wen Dao
Posted 5 hours ago

Thanks for your assistance; the issue is now solved.
POSTED BY: Wen Dao

Assuming Expand[] will separate terms as it does in eq1:

eq1 = 2 (a + b) == E^(2 a) + 2 Log[b] + 1;
GatherBy[List @@ Expand[Subtract @@ eq1], FreeQ[b]] //
 Replace[{{lhs_, rhs_} :> Plus @@ lhs == -Plus @@ rhs,
   {oneside_} :> oneside == 0}]

(*  -1 + 2 a - E^(2 a) == -2 b + 2 Log[b]  *)
POSTED BY: Michael Rogers
Wen Dao
Wen Dao
Posted 5 hours ago

Perfect！ thanks to your approach—the issue is now resolved.
POSTED BY: Wen Dao

You can use AddSides or SubtractSides. http://reference.wolfram.com/language/guide/ManipulatingEquations.html
POSTED BY: Gianluca Gorni
Wen Dao
Wen Dao
Posted 5 hours ago

Okay, these two functions are useful for transposing the equation.
POSTED BY: Wen Dao
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard