2.141   ODE No. 141

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

\[ a x y(x)+b+x^2 \left (y'(x)+y(x)^2\right )=0 \] Mathematica : cpu = 0.169393 (sec), leaf count = 67

\[\left \{\left \{y(x)\to -\frac {a}{2 x}-\frac {-1+\sqrt {a^2-2 a-4 b+1} \left (-1+\frac {2 c_1}{x^{\sqrt {a^2-2 a-4 b+1}}+c_1}\right )}{2 x}\right \}\right \}\] Maple : cpu = 0.063 (sec), leaf count = 51

\[\left \{y \left (x \right ) = \frac {-a -\sqrt {a^{2}-2 a -4 b +1}\, \tanh \left (\frac {\sqrt {a^{2}-2 a -4 b +1}\, \left (c_{1}-\ln \left (x \right )\right )}{2}\right )+1}{2 x}\right \}\]