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 = 0.0674344 (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 = 0.292 (sec), leaf count = 74

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