2.302   ODE No. 302

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

\[ \left (x^2 y(x)^2+x\right ) y'(x)+y(x)=0 \] Mathematica : cpu = 0.122219 (sec), leaf count = 70

\[\left \{\left \{y(x)\to \frac {c_1 x-\sqrt {x} \sqrt {4+c_1{}^2 x}}{2 x}\right \},\left \{y(x)\to \frac {c_1 x+\sqrt {x} \sqrt {4+c_1{}^2 x}}{2 x}\right \}\right \}\] Maple : cpu = 0.134 (sec), leaf count = 133

\[\left \{y \left (x \right ) = -\frac {\sqrt {-2 c_{1} \left (-2 c_{1}-x +\sqrt {\left (4 c_{1}+x \right ) x}\right ) x}}{2 c_{1} x}, y \left (x \right ) = \frac {\sqrt {-2 c_{1} \left (-2 c_{1}-x +\sqrt {\left (4 c_{1}+x \right ) x}\right ) x}}{2 c_{1} x}, y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {c_{1} \left (2 c_{1}+x +\sqrt {\left (4 c_{1}+x \right ) x}\right ) x}}{2 c_{1} x}, y \left (x \right ) = \frac {\sqrt {2}\, \sqrt {c_{1} \left (2 c_{1}+x +\sqrt {\left (4 c_{1}+x \right ) x}\right ) x}}{2 c_{1} x}\right \}\]