\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x}) \left (\frac {\text {Global$\grave { }$e1} (\text {Global$\grave { }$a}+\text {Global$\grave { }$x})}{\left ((\text {Global$\grave { }$a}+\text {Global$\grave { }$x})^2+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2\right )^{3/2}}+\frac {\text {Global$\grave { }$e2} (\text {Global$\grave { }$x}-\text {Global$\grave { }$a})}{\left ((\text {Global$\grave { }$x}-\text {Global$\grave { }$a})^2+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2\right )^{3/2}}\right )-\text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \left (\frac {\text {Global$\grave { }$e1}}{\left ((\text {Global$\grave { }$a}+\text {Global$\grave { }$x})^2+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2\right )^{3/2}}+\frac {\text {Global$\grave { }$e2}}{\left ((\text {Global$\grave { }$x}-\text {Global$\grave { }$a})^2+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2\right )^{3/2}}\right )=0 \] ✗ Mathematica : cpu = 300.207 (sec), leaf count = 0 , could not solve
DSolve[-(Global`y[Global`x]*(Global`e2/((-Global`a + Global`x)^2 + Global`y[Global`x]^2)^(3/2) + Global`e1/((Global`a + Global`x)^2 + Global`y[Global`x]^2)^(3/2))) + ((Global`e2*(-Global`a + Global`x))/((-Global`a + Global`x)^2 + Global`y[Global`x]^2)^(3/2) + (Global`e1*(Global`a + Global`x))/((Global`a + Global`x)^2 + Global`y[Global`x]^2)^(3/2))*Derivative[1][Global`y][Global`x] == 0, Global`y[Global`x], Global`x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , exception
time expired