2.299   ODE No. 299

$\left (3 x y(x)^2-x^2\right ) y'(x)+y(x)^3-2 x y(x)=0$ Mathematica : cpu = 0.106773 (sec), leaf count = 371

$\left \{\left \{y(x)\to -\frac {\sqrt [3]{\frac {2}{3}} x^2}{\sqrt [3]{9 c_1 x^2+\sqrt {3} \sqrt {27 c_1{}^2 x^4-4 x^9}}}-\frac {\sqrt [3]{9 c_1 x^2+\sqrt {3} \sqrt {27 c_1{}^2 x^4-4 x^9}}}{\sqrt [3]{2} 3^{2/3} x}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) x^2}{2^{2/3} \sqrt [3]{3} \sqrt [3]{9 c_1 x^2+\sqrt {3} \sqrt {27 c_1{}^2 x^4-4 x^9}}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{9 c_1 x^2+\sqrt {3} \sqrt {27 c_1{}^2 x^4-4 x^9}}}{2 \sqrt [3]{2} 3^{2/3} x}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) x^2}{2^{2/3} \sqrt [3]{3} \sqrt [3]{9 c_1 x^2+\sqrt {3} \sqrt {27 c_1{}^2 x^4-4 x^9}}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{9 c_1 x^2+\sqrt {3} \sqrt {27 c_1{}^2 x^4-4 x^9}}}{2 \sqrt [3]{2} 3^{2/3} x}\right \}\right \}$ Maple : cpu = 0.174 (sec), leaf count = 276

$\left \{ y \left ( x \right ) =-{\frac {{12}^{{\frac {2}{3}}}}{144\,x} \left ( \left ( -12\,i{x}^{3}+i \left ( \left ( 12\,\sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+108\,{\it \_C1} \right ) {x}^{2} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+12\,{x}^{3}+ \left ( \left ( 12\,\sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+108\,{\it \_C1} \right ) {x}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( \sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+9\,{\it \_C1} \right ) {x}^{2}}}}},y \left ( x \right ) ={\frac {{12}^{{\frac {2}{3}}}}{144\,x} \left ( -12\,i\sqrt {3}{x}^{3}+i\sqrt {3} \left ( \left ( 12\,\sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+108\,{\it \_C1} \right ) {x}^{2} \right ) ^{{\frac {2}{3}}}-12\,{x}^{3}- \left ( \left ( 12\,\sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+108\,{\it \_C1} \right ) {x}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( \sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+9\,{\it \_C1} \right ) {x}^{2}}}}},y \left ( x \right ) ={\frac {1}{6\,x}\sqrt [3]{ \left ( 12\,\sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+108\,{\it \_C1} \right ) {x}^{2}}}+2\,{\frac {{x}^{2}}{\sqrt [3]{ \left ( 12\,\sqrt {-12\,{x}^{5}+81\,{{\it \_C1}}^{2}}+108\,{\it \_C1} \right ) {x}^{2}}}} \right \}$