2.246   ODE No. 246

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

\[ x (3 y(x)+2 x) y'(x)+3 (y(x)+x)^2=0 \] Mathematica : cpu = 0.132207 (sec), leaf count = 80

\[\left \{\left \{y(x)\to \frac {1}{6} \left (-4 x-\frac {\sqrt {2} \sqrt {-x^4+3 e^{4 c_1}}}{x}\right )\right \},\left \{y(x)\to \frac {1}{6} \left (-4 x+\frac {\sqrt {2} \sqrt {-x^4+3 e^{4 c_1}}}{x}\right )\right \}\right \}\] Maple : cpu = 0.053 (sec), leaf count = 63

\[ \left \{ y \left ( x \right ) ={\frac {1}{6\,{\it \_C1}\,x} \left ( -4\,{\it \_C1}\,{x}^{2}-\sqrt {-2\,{x}^{4}{{\it \_C1}}^{2}+6} \right ) },y \left ( x \right ) ={\frac {1}{6\,{\it \_C1}\,x} \left ( -4\,{\it \_C1}\,{x}^{2}+\sqrt {-2\,{x}^{4}{{\it \_C1}}^{2}+6} \right ) } \right \} \]