# Question:why PDEtools:-Solve hangs, but solve does not on this problem?

## Question:why PDEtools:-Solve hangs, but solve does not on this problem?

Maple 2020

These are 4 equations in 4 unknowns. the equations are kinda long. But the issue is that PDEtools:-Solve hangs, while solve finishes instantly.

I have though before that  PDEtools:-Solve is a higher level API which ends up using solve? So why does it hang on this?

```restart;

eqs:=[2 = c1+c2+c4-1, 0 = ((c2+c4-2)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(1/12*c3*3^(1/2)+1/12*c2-1/6*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)+2*c3*3^(1/2)-2*c2+4*c4)/(108+12*59^(1/2)*3^(1/2))^(1/3), -1 = -1/6/(108+12*59^(1/2)*3^(1/2))^(2/3)*((((c2-2*c4)*3^(1/2)-3*c3)*59^(1/2)-33*c3*3^(1/2)+33*c2-66*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(2*c2+2*c4+12)*(108+12*59^(1/2)*3^(1/2))^(2/3)+((-12*c2+24*c4)*3^(1/2)-36*c3)*59^(1/2)-60*c3*3^(1/2)-60*c2+120*c4), -5 = ((((2*c2-4*c4)*3^(1/2)+6*c3)*59^(1/2)-30*c3*3^(1/2)-30*c2+60*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(((-c2+2*c4)*3^(1/2)+3*c3)*59^(1/2)+13*c3*3^(1/2)-13*c2+26*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)-96*(59^(1/2)*3^(1/2)+9)*(c2+c4))/(24*59^(1/2)*3^(1/2)+216)];

unknowns:=[c1, c2, c3, c4];

#han to put a timelimit, else it will never finish. I waited 20 minutes before.
timelimit(30,PDEtools:-Solve(eqs,unknowns));

#this completes right away
solve(eqs,unknowns);
```

Is this a known issue and to be expected sometimes?

 > restart;
 > interface(version);

 > Physics:-Version();

 > eqs:=[2 = c1+c2+c4-1, 0 = ((c2+c4-2)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(1/12*c3*3^(1/2)+1/12*c2-1/6*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)+2*c3*3^(1/2)-2*c2+4*c4)/(108+12*59^(1/2)*3^(1/2))^(1/3), -1 = -1/6/(108+12*59^(1/2)*3^(1/2))^(2/3)*((((c2-2*c4)*3^(1/2)-3*c3)*59^(1/2)-33*c3*3^(1/2)+33*c2-66*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(2*c2+2*c4+12)*(108+12*59^(1/2)*3^(1/2))^(2/3)+((-12*c2+24*c4)*3^(1/2)-36*c3)*59^(1/2)-60*c3*3^(1/2)-60*c2+120*c4), -5 = ((((2*c2-4*c4)*3^(1/2)+6*c3)*59^(1/2)-30*c3*3^(1/2)-30*c2+60*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(((-c2+2*c4)*3^(1/2)+3*c3)*59^(1/2)+13*c3*3^(1/2)-13*c2+26*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)-96*(59^(1/2)*3^(1/2)+9)*(c2+c4))/(24*59^(1/2)*3^(1/2)+216)]; unknowns:=[c1, c2, c3, c4];

 > timelimit(30,PDEtools:-Solve(eqs,unknowns))

Error, (in expand/bigprod) time expired

 > solve(eqs,unknowns):
 >