2.400   ODE No. 400

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

\[ -2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0 \] Mathematica : cpu = 0.482087 (sec), leaf count = 135

\[\left \{\text {Solve}\left [\frac {1}{3} \log (y(x))-\frac {2 \sqrt {x^4-6 x y(x)} \tanh ^{-1}\left (\frac {x^{3/2}}{\sqrt {x^3-6 y(x)}}\right )}{3 \sqrt {x} \sqrt {x^3-6 y(x)}}=c_1,y(x)\right ],\text {Solve}\left [\frac {2 \sqrt {x^4-6 x y(x)} \tanh ^{-1}\left (\frac {x^{3/2}}{\sqrt {x^3-6 y(x)}}\right )}{3 \sqrt {x} \sqrt {x^3-6 y(x)}}+\frac {1}{3} \log (y(x))=c_1,y(x)\right ]\right \}\] Maple : cpu = 0.186 (sec), leaf count = 74

\[\left \{y \left (x \right ) = \frac {x^{3}}{6}, y \left (x \right ) = \frac {-\sqrt {-6 c_{1} x}\, x +3}{3 c_{1}}, y \left (x \right ) = \frac {\sqrt {-6 c_{1} x}\, x +3}{3 c_{1}}, y \left (x \right ) = c_{1}-\frac {\sqrt {-6 c_{1} x}\, x}{3}, y \left (x \right ) = c_{1}+\frac {\sqrt {-6 c_{1} x}\, x}{3}\right \}\]