Group Abstract

Message Boards

WOLFRAM COMMUNITY

3.2K Views

4 Replies

2 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Evaluation of solving simultaneous differential equations doesn't end

Anand Mathew

Posted 2 years ago

My code in Mathematica: eqn1 = (M - ((\[Alpha]^2)/\[Beta])) u''[x] + (e - f)* P''[x] + (\[Alpha]/\[Beta])\[Mu]'[x] == 0; eqn2 = (e - f)u''[x] + bP''[x] - aP[x] + (1/q)\[Mu]'[x] == 0; eqn3 = \[Epsilon]r\[Mu]''[x] + (1/(\[Lambda]^2))\[Mu][ x] - (1/(\[Lambda]^2))(\[Mu]hat + \[Alpha]*u'[x]) == 0; DSolve[{eqn1, eqn2, eqn3}, {u[x], P[x], \[Mu][x]}, x] I ran this for almost a day but didnt give any results, also there are no errors. I am not sure what is wrong? Is the way I have written the equations wrong or are these differential equations unsolvable? Any help would be appreciated. Thanks

My code in Mathematica:

eqn1 = (M - ((\[Alpha]^2)/\[Beta])) u''[x] + (e - f)*
     P''[x] + (\[Alpha]/\[Beta])*\[Mu]'[x] == 0;

eqn2 = (e - f)*u''[x] + b*P''[x] - a*P[x] + (1/q)*\[Mu]'[x] == 0;

eqn3 = \[Epsilon]r*\[Mu]''[x] + (1/(\[Lambda]^2))*\[Mu][
      x] - (1/(\[Lambda]^2))*(\[Mu]hat + \[Alpha]*u'[x]) == 0;

DSolve[{eqn1, eqn2, eqn3}, {u[x], P[x], \[Mu][x]}, x]

I ran this for almost a day but didnt give any results, also there are no errors. I am not sure what is wrong? Is the way I have written the equations wrong or are these differential equations unsolvable? Any help would be appreciated. Thanks

POSTED BY: Anand Mathew

4 Replies

Sort By:

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 2 years ago

The problem seems to be too many free parameters. You can solve one equation at a time: sol1 = DSolve[eqn1, u, x][[1]] sol2 = DSolve[Simplify[eqn2 /. sol1], P, x] sol3 = DSolve[Simplify[eqn3 /. sol1 /. sol2], \[Mu][x], x]