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 = 0.204838 (sec), leaf count = 101

\[\left \{\left \{y(x)\to \frac {2 x^3-\sqrt {e^{4 c_1} x^2-3 e^{2 c_1} x^4}}{x^2+e^{2 c_1}}\right \},\left \{y(x)\to \frac {2 x^3+\sqrt {e^{4 c_1} x^2-3 e^{2 c_1} x^4}}{x^2+e^{2 c_1}}\right \}\right \}\] Maple : cpu = 0.25 (sec), leaf count = 65

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