2.299   ODE No. 299

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left (3 x y(x)^2-x^2\right ) y'(x)+y(x)^3-2 x y(x)=0 \] Mathematica : cpu = 0.0243934 (sec), leaf count = 328

\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{2} \left (9 c_1 x^2+\sqrt {81 c_1^2 x^4-12 x^9}\right ){}^{2/3}+2 \sqrt [3]{3} x^3}{6^{2/3} x \sqrt [3]{9 c_1 x^2+\sqrt {81 c_1^2 x^4-12 x^9}}}\right \},\left \{y(x)\to \frac {\sqrt [3]{3} \left (1-i \sqrt {3}\right ) \left (18 c_1 x^2+2 \sqrt {81 c_1^2 x^4-12 x^9}\right ){}^{2/3}+2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) x^3}{12 x \sqrt [3]{9 c_1 x^2+\sqrt {81 c_1^2 x^4-12 x^9}}}\right \},\left \{y(x)\to \frac {\sqrt [3]{3} \left (1+i \sqrt {3}\right ) \left (18 c_1 x^2+2 \sqrt {81 c_1^2 x^4-12 x^9}\right ){}^{2/3}+2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) x^3}{12 x \sqrt [3]{9 c_1 x^2+\sqrt {81 c_1^2 x^4-12 x^9}}}\right \}\right \}\]

Maple : cpu = 0.183 (sec), leaf count = 276

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