2.259   ODE No. 259

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

\[ 2 x^2 y(x) y'(x)-e^{x-\frac {1}{x}} x^2-y(x)^2=0 \] Mathematica : cpu = 0.282333 (sec), leaf count = 50

\[\left \{\left \{y(x)\to -e^{\left .-\frac {1}{2}\right /x} \sqrt {e^x+c_1}\right \},\left \{y(x)\to e^{\left .-\frac {1}{2}\right /x} \sqrt {e^x+c_1}\right \}\right \}\] Maple : cpu = 0.033 (sec), leaf count = 51

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