#### 2.244   ODE No. 244

$x (2 y(x)-x-1) y'(x)+(-y(x)+2 x-1) y(x)=0$ Mathematica : cpu = 11.1231 (sec), leaf count = 484

$\left \{\left \{y(x)\to -\frac {\sqrt [3]{2} x}{\sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}-\frac {\sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}{3 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}{6 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}{6 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \}\right \}$ Maple : cpu = 0.094 (sec), leaf count = 391

$\left \{ y \left ( x \right ) ={\frac {3}{80\,{\it \_C1}} \left ( \left ( x \left ( \sqrt {5}\sqrt {{\frac {80\, \left ( 1+x \right ) ^{2}{\it \_C1}-x}{{\it \_C1}}}}-20\,x-20 \right ) {{\it \_C1}}^{2} \right ) ^{{\frac {2}{3}}} \left ( i\sqrt {3}-1 \right ) \sqrt [3]{5}- \left ( x \left ( 1+i\sqrt {3} \right ) {5}^{{\frac {2}{3}}}+{\frac {80+80\,x}{3}\sqrt [3]{-20\,x \left ( -1/20\,\sqrt {5}\sqrt {{\frac {80\, \left ( 1+x \right ) ^{2}{\it \_C1}-x}{{\it \_C1}}}}+x+1 \right ) {{\it \_C1}}^{2}}} \right ) {\it \_C1} \right ) {\frac {1}{\sqrt [3]{-20\,x \left ( -1/20\,\sqrt {5}\sqrt {{\frac {80\, \left ( 1+x \right ) ^{2}{\it \_C1}-x}{{\it \_C1}}}}+x+1 \right ) {{\it \_C1}}^{2}}}}},y \left ( x \right ) =-{\frac {3}{80\,{\it \_C1}} \left ( \left ( 1+i\sqrt {3} \right ) \left ( x \left ( \sqrt {5}\sqrt {{\frac {80\, \left ( 1+x \right ) ^{2}{\it \_C1}-x}{{\it \_C1}}}}-20\,x-20 \right ) {{\it \_C1}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt [3]{5}- \left ( x \left ( i\sqrt {3}-1 \right ) {5}^{{\frac {2}{3}}}-{\frac {80+80\,x}{3}\sqrt [3]{-20\,x \left ( -1/20\,\sqrt {5}\sqrt {{\frac {80\, \left ( 1+x \right ) ^{2}{\it \_C1}-x}{{\it \_C1}}}}+x+1 \right ) {{\it \_C1}}^{2}}} \right ) {\it \_C1} \right ) {\frac {1}{\sqrt [3]{-20\,x \left ( -1/20\,\sqrt {5}\sqrt {{\frac {80\, \left ( 1+x \right ) ^{2}{\it \_C1}-x}{{\it \_C1}}}}+x+1 \right ) {{\it \_C1}}^{2}}}}},y \left ( x \right ) ={\frac {3\,\sqrt [3]{5}}{40\,{\it \_C1}}\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{\it \_C1}\,{x}^{2}+160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}-20\,x-20 \right ) {{\it \_C1}}^{2}}}+{\frac {3\,x{5}^{2/3}}{40}{\frac {1}{\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{\it \_C1}\,{x}^{2}+160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}-20\,x-20 \right ) {{\it \_C1}}^{2}}}}}-1-x \right \}$