MATLAB: Vpasolve and independent equations

independent equationsvpasolve

Hello,
How does the vpasolve command work and what is the difference between vpasolve and solve ?
I read on a discussion the vpasolve can solve many independent equations without using a loop over single equations. Then I tried and got the following.
>> syms x y z u;
1>> sol = vpasolve([2*x+3, exp(y)-20,log(z+5)+60],[x,y,z]);[sol.x sol.y sol.z] % correct answer

 
ans =
 
[ -1.5, 2.9957322735539909934352235761425, -4.9999999999999999999999999912435]
2>> sol = vpasolve([2*x+3, exp(y)-20,log(z+5)+60,1/u+10],[x,y,z,u]);[sol.x sol.y sol.z sol.u] % ??

 
ans =
 
[ -1.5, 72.364158219472484524557308589775, - 2.3427240402068111246084751973687e55 - 3.8942786692210248849674644994505e53i, 2.1973620198615687196267013300432e220164446]
3>> sol = vpasolve([2*x+3, exp(y)-20,1/u+10],[x,y,u]);[sol.x sol.y sol.u] % ??
 
ans =
 
[ -1.5, 72.395408219472484524557308589775, 7.6288584990871366247428709032065e187034710]
4>> sol = vpasolve([2*x+3,1/u+10],[x,u]);[sol.x sol.u] % correct answer
 
ans =
 
[ -1.5, -0.1]
Commands 1 and 4 gave the correct answer that I expected. But I don't understand the results of 2 and 3. 2 is the 1 to which I added one simple equation 1/u+10 ==0. Not only the result of that equation is not correct (in the sens -1/10 that I expect) but also the results of the former equations are affected. I cannot uderstand complex number as result for log(z+5)+60==0. Same thing in 3. then in 4 I supress some equations and I get expected results again. Does anyone understand what is actually done ?
And in the case, how can I solve for many independent equations (like the same equations but with different parameters: e.g. a1*x+b1==0, a2*x+b2==0, …, an*x+bn ==0) without using a loop over the single equations ?
Thanks.

Best Answer

‘vpasolve’ solves algebraic equations using numerical methods whereas ‘solve’ solves the equations symbolically. If possible, solve equations symbolically using ‘solve’, and then approximate the obtained symbolic results numerically using ‘vpa’.
You can solve multiple independent equations by using the following piece of code: 
syms x y z u; 
eqns = [2*x+3==0, exp(y)-20==0,log(z+5)+60==0,1/u+10==0]; 
vars = [x,y,z,u]; 
[x1,y1,z1,u1]=solve(eqns,vars);
For further details on ‘solve’ and ‘vpa’ functions refer the following links:
https://www.mathworks.com/help/symbolic/solve.html
https://www.mathworks.com/help/symbolic/vpa.html
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