#### 2.270   ODE No. 270

$x^2+\left (y(x)^2-x\right ) y'(x)-y(x)=0$ Mathematica : cpu = 0.124156 (sec), leaf count = 327

$\left \{\left \{y(x)\to -\frac {3 \sqrt [3]{2} x}{\sqrt [3]{\sqrt {\left (81 c_1+27 x^3\right ){}^2-2916 x^3}+81 c_1+27 x^3}}-\frac {\sqrt [3]{\sqrt {\left (81 c_1+27 x^3\right ){}^2-2916 x^3}+81 c_1+27 x^3}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {3 \left (1+i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{\sqrt {\left (81 c_1+27 x^3\right ){}^2-2916 x^3}+81 c_1+27 x^3}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (81 c_1+27 x^3\right ){}^2-2916 x^3}+81 c_1+27 x^3}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {3 \left (1-i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{\sqrt {\left (81 c_1+27 x^3\right ){}^2-2916 x^3}+81 c_1+27 x^3}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (81 c_1+27 x^3\right ){}^2-2916 x^3}+81 c_1+27 x^3}}{6 \sqrt [3]{2}}\right \}\right \}$ Maple : cpu = 0.02 (sec), leaf count = 319

$\left \{ y \left ( x \right ) ={\frac {1}{2} \left ( \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) =-{\frac {1}{4} \left ( \left ( i \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,ix \right ) \sqrt {3}+ \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) ={\frac {1}{4} \left ( i \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}\sqrt {3}-4\,i\sqrt {3}x- \left ( -4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( 6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}} \right \}$