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 = 0.235558 (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 = 0.021 (sec), leaf count = 51

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