2.1834   ODE No. 1834

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

\[ \left (x^2 y(x) y''(x)+x^2 \left (-y'(x)^2\right )+y(x)^2\right )^2-4 x y(x) \left (x y'(x)-y(x)\right )^3=0 \] Mathematica : cpu = 22.6742 (sec), leaf count = 19

\[\left \{\left \{y(x)\to c_1 x e^{\frac {1}{-x+c_2}}\right \}\right \}\] Maple : cpu = 0.652 (sec), leaf count = 92

\[\left \{y \left (x \right ) = 0, y \left (x \right ) = c_{1} x, y \left (x \right ) = \mathit {ODESolStruc} \left ({\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {2 \sqrt {\left (\textit {\_a} \textit {\_}b\left (\textit {\_a} \right )-1\right ) \textit {\_a}}\, \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )-2 \sqrt {\left (\textit {\_a} \textit {\_}b\left (\textit {\_a} \right )-1\right ) \textit {\_a}}-1}{\textit {\_a}^{2}}\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=\frac {\frac {d}{d x}y \left (x \right )}{y \left (x \right )}\right \}, \left \{x =\textit {\_a} , y \left (x \right )={\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]