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 = 0.044855 (sec), leaf count = 192

\[\left \{\left \{y(x)\to \frac {1}{x \left (-\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {c_1-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}}}-\frac {a}{-a^2-a x^2-b x^2}\right )}-\frac {a+x^2}{x}\right \},\left \{y(x)\to \frac {1}{x \left (\frac {x}{\left (a^2+a x^2+b x^2\right )^{3/2} \sqrt {c_1-\frac {1}{(a+b) \left (a^2+a x^2+b x^2\right )}}}-\frac {a}{-a^2-a x^2-b x^2}\right )}-\frac {a+x^2}{x}\right \}\right \}\] Maple : cpu = 0.085 (sec), leaf count = 93

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