2.262   ODE No. 262

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

\[ 2 x^3+\left (2 x^2 y(x)-x^3\right ) y'(x)-4 x y(x)^2+y(x)^3=0 \] Mathematica : cpu = 0.0696845 (sec), leaf count = 101

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

Maple : cpu = 0.371 (sec), leaf count = 65

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