\[ \left (x^2 y(x)-1\right ) y'(x)-x y(x)^2+1=0 \] ✓ Mathematica : cpu = 8.68071 (sec), leaf count = 819
DSolve[1 - x*y[x]^2 + (-1 + x^2*y[x])*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {6 x c_1-x}{6 c_1-1}+\frac {\sqrt [3]{-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+54\right ){}^2}+54}}{3 \sqrt [3]{2} (6 c_1-1)}-\frac {\sqrt [3]{2} \left (54 x^2 c_1-9 x^2\right )}{3 (6 c_1-1) \sqrt [3]{-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+54\right ){}^2}+54}}\right \},\left \{y(x)\to \frac {6 x c_1-x}{6 c_1-1}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+54\right ){}^2}+54}}{6 \sqrt [3]{2} (6 c_1-1)}+\frac {\left (1+i \sqrt {3}\right ) \left (54 x^2 c_1-9 x^2\right )}{3\ 2^{2/3} (6 c_1-1) \sqrt [3]{-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+54\right ){}^2}+54}}\right \},\left \{y(x)\to \frac {6 x c_1-x}{6 c_1-1}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+54\right ){}^2}+54}}{6 \sqrt [3]{2} (6 c_1-1)}+\frac {\left (1-i \sqrt {3}\right ) \left (54 x^2 c_1-9 x^2\right )}{3\ 2^{2/3} (6 c_1-1) \sqrt [3]{-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1{}^2 x^3+648 c_1 x^3-54 x^3+1944 c_1{}^2-648 c_1+54\right ){}^2}+54}}\right \}\right \}\] ✓ Maple : cpu = 0.654 (sec), leaf count = 1338
dsolve((x^2*y(x)-1)*diff(y(x),x)-x*y(x)^2+1 = 0,y(x))
\[y \left (x \right ) = \frac {\left (\left (-c_{1}+80\right ) x^{7}-160 x^{4}+80 x \right ) 4^{\frac {1}{3}} \left (\left (-\frac {1}{4}+\sqrt {\frac {-5 x^{6}+10 x^{3}-5}{-80+\left (c_{1}-80\right ) x^{6}+160 x^{3}}}\right ) c_{1} \left (-80+\left (c_{1}-80\right ) x^{6}+160 x^{3}\right )^{2}\right )^{\frac {1}{3}}+\left (c_{1}^{2}-80 c_{1}\right ) x^{8}+160 c_{1} x^{5}-80 x^{2} c_{1}+\left (c_{1} \left (-1+4 \sqrt {\frac {-5 x^{6}+10 x^{3}-5}{-80+\left (c_{1}-80\right ) x^{6}+160 x^{3}}}\right ) \left (x^{6} c_{1}-80 x^{6}+160 x^{3}-80\right )^{2}\right )^{\frac {2}{3}}}{\left (80+\left (-c_{1}+80\right ) x^{6}-160 x^{3}\right ) 4^{\frac {1}{3}} \left (\left (-\frac {1}{4}+\sqrt {\frac {-5 x^{6}+10 x^{3}-5}{-80+\left (c_{1}-80\right ) x^{6}+160 x^{3}}}\right ) c_{1} \left (-80+\left (c_{1}-80\right ) x^{6}+160 x^{3}\right )^{2}\right )^{\frac {1}{3}}+x^{2} \left (\left (c_{1}^{2}-80 c_{1}\right ) x^{8}+160 c_{1} x^{5}-80 x^{2} c_{1}+\left (c_{1} \left (-1+4 \sqrt {\frac {-5 x^{6}+10 x^{3}-5}{-80+\left (c_{1}-80\right ) x^{6}+160 x^{3}}}\right ) \left (x^{6} c_{1}-80 x^{6}+160 x^{3}-80\right )^{2}\right )^{\frac {2}{3}}\right )}\]