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 = 0.0925387 (sec), leaf count = 72

\[\left \{\left \{y(x)\to \frac {\sqrt [3]{x^2+c_1}}{\sqrt [3]{x}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}}\right \}\right \}\] Maple : cpu = 0.014 (sec), leaf count = 73

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