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Help with rearranging the equation and solution Steps?

Sami Heidari

Posted 1 day ago

Hi, How can I rearrange the equation eq1 in terms of (H + Derivative[1][G][[Xi]]/G[[Xi]]^2) and then solve for it?

POSTED BY: Sami Heidari

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 1 day ago

Your presumed solution contain `C,B,beta`, while the equation has no such variables. You can check the solutions given by Mathematica: eq1 /. Solve[ coefficients == 0, {a0, a1, a2, a3, a4, H, \[Nu]}] // Simplify and they are fine.

POSTED BY: Gianluca Gorni

Sami Heidari

Posted 1 day ago

Yes, you are right; I made some mistakes in certain parts. I just have one question: If I want to rearrange an equation I have in terms of that expression mentioned in the first question, so that there are no functions within the equation, what should I do?

POSTED BY: Sami Heidari

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 1 day ago

Sorry, I don't understand your question.

POSTED BY: Gianluca Gorni

Sami Heidari

Posted 1 day ago

I don't know why the placement isn't happening? dG[\[Xi]_] := D[G[\[Xi]], \[Xi]]; \[CapitalXi]dG[\[Xi]_] := dG[\[Xi]]/G[\[Xi]]^2; D[\[CapitalXi]dG[\[Xi]], \[Xi]] = A + B \[CapitalXi]dG[\[Xi]]^2 + c \[CapitalXi]dG[\[Xi]]; a = {a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20}; U[\[Xi]_] := Sum[a[[i + 3]](H + \[CapitalXi]dG[\[Xi]])^i, {i, p, q}] p = -1; q = 1; U[\[Xi]] eq1 = 2(\[Nu]^2 - k^2)D[U[\[Xi]], \[Xi]] + 2 (\[Alpha] k^2 \[Nu]^2)D[U[\[Xi]], {\[Xi], 2}] - 3 \[Nu] k^2*D[U[\[Xi]], \[Xi]]^2 // Expand

I don't know why the placement isn't happening?

dG[\[Xi]_] := D[G[\[Xi]], \[Xi]];
\[CapitalXi]dG[\[Xi]_] := dG[\[Xi]]/G[\[Xi]]^2;
D[\[CapitalXi]dG[\[Xi]], \[Xi]] = 
  A + B \[CapitalXi]dG[\[Xi]]^2 + c \[CapitalXi]dG[\[Xi]]; 


a = {a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, 
   a15, a16, a17, a18, a19, a20};


U[\[Xi]_] := Sum[a[[i + 3]]*(H + \[CapitalXi]dG[\[Xi]])^i, {i, p, q}]
p = -1; q = 1;
U[\[Xi]]
eq1 = 2*(\[Nu]^2 - k^2)*D[U[\[Xi]], \[Xi]] + 
   2 (\[Alpha] k^2 \[Nu]^2)*D[U[\[Xi]], {\[Xi], 2}] - 
   3 \[Nu] k^2*D[U[\[Xi]], \[Xi]]^2 // Expand

POSTED BY: Sami Heidari

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 1 day ago

What placement? Your third line cannot work with = . Maybe you meant it as an equation? dG = G'; \[CapitalXi]dG[\[Xi]_] := dG[\[Xi]]/G[\[Xi]]^2; \[CapitalXi]dG'[\[Xi]] == A + B \[CapitalXi]dG[\[Xi]]^2 + c \[CapitalXi]dG[\[Xi]]

POSTED BY: Gianluca Gorni

Sami Heidari

Posted 1 day ago

Yes, I want the expressions that I defined above in section eq1 to be substituted into this equation, but when I run the code, the substitution does not occur.???

POSTED BY: Sami Heidari

Sami Heidari

Posted 1 day ago

In order to obtain an algebraic system, one must set the coeffcients of (H + G′/G2)i to zero. Solve the obtained algebraic system. But the expressions were not arranged correctly, no answer was obtained, while the answer was as follows: