ODE No. 740

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

\[ y'(x)=\frac {x^4-2 x^2 y(x)^2+y(x)^4+x}{y(x)} \] Mathematica : cpu = 0.0610398 (sec), leaf count = 74

\[\left \{\left \{y(x)\to -\frac {\sqrt {2 c_1 x^2+2 x^3-1}}{\sqrt {2} \sqrt {c_1+x}}\right \},\left \{y(x)\to \frac {\sqrt {2 c_1 x^2+2 x^3-1}}{\sqrt {2} \sqrt {c_1+x}}\right \}\right \}\] Maple : cpu = 0.107 (sec), leaf count = 72

\[ \left \{ y \left ( x \right ) ={\frac {\sqrt {2}}{2\,{\it \_C1}+2\,x}\sqrt { \left ( {\it \_C1}+x \right ) \left ( 2\,{\it \_C1}\,{x}^{2}+2\,{x}^{3}-1 \right ) }},y \left ( x \right ) =-{\frac {\sqrt {2}}{2\,{\it \_C1}+2\,x}\sqrt { \left ( {\it \_C1}+x \right ) \left ( 2\,{\it \_C1}\,{x}^{2}+2\,{x}^{3}-1 \right ) }} \right \} \]