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 = 0.234607 (sec), leaf count = 192

\[\left \{\left \{y(x)\to -\frac {a+x^2}{x}+\frac {1}{x \left (-\frac {a}{-a^2-a x^2-b x^2}-\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}+c_1}}\right )}\right \},\left \{y(x)\to -\frac {a+x^2}{x}+\frac {1}{x \left (-\frac {a}{-a^2-a x^2-b x^2}+\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}+c_1}}\right )}\right \}\right \}\] Maple : cpu = 0.055 (sec), leaf count = 93

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