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 = 0.0935685 (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 = 0.112 (sec), leaf count = 133

\[ \left \{ y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}\,x}\sqrt {-2\,x{\it \_C1}\, \left ( -2\,{\it \_C1}-x+\sqrt {x \left ( 4\,{\it \_C1}+x \right ) } \right ) }},y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}\,x}\sqrt {-2\,x{\it \_C1}\, \left ( -2\,{\it \_C1}-x+\sqrt {x \left ( 4\,{\it \_C1}+x \right ) } \right ) }},y \left ( x \right ) =-{\frac {\sqrt {2}}{2\,{\it \_C1}\,x}\sqrt {x{\it \_C1}\, \left ( 2\,{\it \_C1}+x+\sqrt {x \left ( 4\,{\it \_C1}+x \right ) } \right ) }},y \left ( x \right ) ={\frac {\sqrt {2}}{2\,{\it \_C1}\,x}\sqrt {x{\it \_C1}\, \left ( 2\,{\it \_C1}+x+\sqrt {x \left ( 4\,{\it \_C1}+x \right ) } \right ) }} \right \} \]