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 = 0.786534 (sec), leaf count = 73

\[\text {Solve}\left [-\frac {i a}{x}=\frac {2 e^{-\frac {(a y(x)+x)^2}{2 x^2 y(x)^2}}}{2 c_1-i \sqrt {2 \pi } \text {erf}\left (\frac {a y(x)+x}{\sqrt {2} x y(x)}\right )},y(x)\right ]\]

Maple : cpu = 0.189 (sec), leaf count = 84

\[ \left \{ {\frac {1}{2} \left ( a\sqrt {\pi }\sqrt {2}{\it Erf} \left ( {\frac {\sqrt {2} \left ( ay \left ( x \right ) +x \right ) }{2\,xy \left ( x \right ) }} \right ) {{\rm e}^{{\frac { \left ( ay \left ( x \right ) +x \right ) ^{2}}{2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}}+2\,x \right ) {{\rm e}^{-{\frac { \left ( \left ( x+a \right ) y \left ( x \right ) +x \right ) \left ( \left ( a-x \right ) y \left ( x \right ) +x \right ) }{2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}}}+{\it \_C1}=0 \right \} \]