3.262   ODE No. 262

\[ \boxed { \left ( 2\,{x}^{2}y \left ( x \right ) -{x}^{3} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{3}-4\,x \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{3}=0} \]

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

Mathematica: cpu = 0.081510 (sec), leaf count = 101 \[ \left \{\left \{y(x)\to \frac {2 x^3-\sqrt {e^{4 c_1} x^2-3 e^{2 c_1} x^4}}{e^{2 c_1}+x^2}\right \},\left \{y(x)\to \frac {\sqrt {e^{4 c_1} x^2-3 e^{2 c_1} x^4}+2 x^3}{e^{2 c_1}+x^2}\right \}\right \} \]

Maple: cpu = 0.218 (sec), leaf count = 74 \[ \left \{ y \left ( x \right ) =-{\frac {x}{{x}^{2}{\it \_C1}-1} \left ( - 3\,{x}^{2}{\it \_C1}+\sqrt {3\,{x}^{2}{\it \_C1}+1}+1 \right ) }-x,y \left ( x \right ) ={\frac {x}{{x}^{2}{\it \_C1}-1} \left ( 3\,{x}^{2}{ \it \_C1}+\sqrt {3\,{x}^{2}{\it \_C1}+1}-1 \right ) }-x \right \} \]