2.298   ODE No. 298

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

\[ 3 x y(x)^2 y'(x)+y(x)^3-2 x=0 \] Mathematica : cpu = 0.00929676 (sec), leaf count = 72

\[\left \{\left \{y(x)\to \frac {\sqrt [3]{c_1+x^2}}{\sqrt [3]{x}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{c_1+x^2}}{\sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{c_1+x^2}}{\sqrt [3]{x}}\right \}\right \}\]

Maple : cpu = 0.016 (sec), leaf count = 99

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