2.238   ODE No. 238

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

\[ (a+x (y(x)+x)) y'(x)-b-y(x) (y(x)+x)=0 \] Mathematica : cpu = 0.0431231 (sec), leaf count = 176

\[\left \{\left \{y(x)\to -\frac {-\frac {1}{\frac {a}{a^2+a x^2+b x^2}-\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {c_1-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}}}}+a+x^2}{x}\right \},\left \{y(x)\to -\frac {-\frac {1}{\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {c_1-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}}}+\frac {a}{a^2+a x^2+b x^2}}+a+x^2}{x}\right \}\right \}\]

Maple : cpu = 0.08 (sec), leaf count = 91

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