solving 4 equation with four unknwon

i can't find the sol for this code . what's rong with it ?

syms k m n d

i=.015; o=.016; x=[0.1;0.2;0.3;0.4;0.5]; v=-104.63; t=97;

equ1=d-.5*k*m*n;

equ2=n-m-(2*t)/k;

equ3=(k/4)*(n^2-m^2+i^2-o^2)+d*log((m*o)/(n*i))-t*(m-i-o+n);

equ4=(.25)*(i^2)*x-(-1/v)*((t/3)*(i^3-m^3+o^3-n^3)+.125*k*(i^4-m^4+n^4-o^4)+.5*d*(m^2-i^2+o^2-n^2)); sol=solve(equ1,equ2,equ3,equ4)

Answer 1

[John BG]

introducing your system in muPAD, as you keyed it in the answer, returns

 Warning: 8 equations in 4 variables.

simplifying it to:

• d-.5*k*m*n=0
• n-m-10/k=0
• k*(n^2-m^2)+d*log(m/n)-(m+n)=0
• 1+(m^3+n^3)+k*(n^4-m^4)+d*(m^2-n^2)=0

muPAD return null, kind of can't find answer.

However, if you approximate log(x) (natural or Neper log) by only 1st Taylor series ln(x)~x-1, bear in mind that evaluating ln(x0)~x-x0-1 , then

• d-.5*k*m*n=0
• n-m-10/k=0
• k*(n^2-m^2)+d*(m/n)-1-(m+n)=0
• 1+(m^3+n^3)+k*(n^4-m^4)+d*(m^2-n^2)=0

muPAD returns

Use attached muPAD result file if you want to carry on from here.

If you find this answer of any help solving your question please click on thumbs-up vote above link, thanks in advance

John

[e-mail]

note: d*log(m/n) should be d*m/n-d, not d*m/n-1