# CAS Problem with integrals

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?

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