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I got this problem thrown at me, unfortunately I lack context at the moment but I thought Maple or Mathematica would solve it anyways.

I have a function $f$ over $x$ and $y$ such as this (Maple)

f := (y-1.298*exp(-1.311*x)-.3435*exp(.3602*x))*(x-3.059865611)*(y+1.875*exp(-.8384*x)+0.7033e-1*exp(.838*x))*(y+.5774*x+3.533)*(.1291*x^2+0.475e-1*y^2+.6927*x+.7080)*(y-.5773*x-3.533)*c;

I have boundary condition so that c needs to be determined to satisfy:

$$ \frac{d^2f}{dx^2}+\frac{d^2f}{dy^2} = -2 $$

solution := solve(diff(f, x, x)+diff(f, y, y) = -2, c)
fsubs := subs(c = solution, f)

So far so good, now I want to integrate $$ \int \left(\frac{df}{dy}-y\right) dx $$

integrate(diff(fsubs, y)-y, x)

this is where things no longer work. I may be impatient but I thought ten minutes would be enough.

Any ideas?

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  • $\begingroup$ I have tried Rubi 4.8 on your problem and it failed with a lot of $RecursionLimit::reclim2 errors. $\endgroup$ Aug 25 '15 at 9:13
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    $\begingroup$ Isn't the solve invocation just setting $c=c(x,y) = -2/\nabla^2(f/c)$, not imposing any kind of boundary condition? $\endgroup$
    – Kirill
    Aug 25 '15 at 21:25
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    $\begingroup$ Is $c$ supposed to be a constant or a function of $x$ and $y$? $\endgroup$ Aug 26 '15 at 1:19
  • $\begingroup$ I get $c$ as a function of $x$ and $y$ $\endgroup$ Aug 26 '15 at 8:19

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