2.146   ODE No. 146

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

\[ a y(x)^2+x^2 y'(x)+x y(x)^3=0 \] Mathematica : cpu = 0.991355 (sec), leaf count = 78

\[\text {Solve}\left [-\frac {i a}{x}=\frac {2 e^{\frac {1}{2} \left (-\frac {i a}{x}-\frac {i}{y(x)}\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {i a}{x}-\frac {i}{y(x)}}{\sqrt {2}}\right )+2 c_1},y(x)\right ]\] Maple : cpu = 0.144 (sec), leaf count = 84

\[\left \{c_{1}+\frac {\left (\sqrt {\pi }\, \sqrt {2}\, a \erf \left (\frac {\sqrt {2}\, \left (a y \left (x \right )+x \right )}{2 x y \left (x \right )}\right ) {\mathrm e}^{\frac {\left (a y \left (x \right )+x \right )^{2}}{2 x^{2} y \left (x \right )^{2}}}+2 x \right ) {\mathrm e}^{-\frac {\left (x +\left (a +x \right ) y \left (x \right )\right ) \left (x +\left (a -x \right ) y \left (x \right )\right )}{2 x^{2} y \left (x \right )^{2}}}}{2} = 0\right \}\]