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 = 0.0258419 (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 = 0.167 (sec), leaf count = 327

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