\[ 2 x^2 y(x) y'(x)-e^{x-\frac {1}{x}} x^2-y(x)^2=0 \] ✓ Mathematica : cpu = 0.266419 (sec), leaf count = 50
DSolve[-(E^(-x^(-1) + x)*x^2) - y[x]^2 + 2*x^2*y[x]*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -e^{\left .-\frac {1}{2}\right /x} \sqrt {e^x+c_1}\right \},\left \{y(x)\to e^{\left .-\frac {1}{2}\right /x} \sqrt {e^x+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.036 (sec), leaf count = 51
dsolve(2*x^2*y(x)*diff(y(x),x)-y(x)^2-x^2*exp(x-1/x) = 0,y(x))
\[y \left (x \right ) = \sqrt {{\mathrm e}^{-\frac {1}{x}} c_{1}+{\mathrm e}^{\frac {x^{2}-1}{x}}}\]