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 = 0.121063 (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 = 0.052 (sec), leaf count = 51

\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,x} \left ( -\tanh \left ( {\frac {-\ln \left ( x \right ) +{\it \_C1}}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}} \right ) \sqrt {{a}^{2}-2\,a-4\,b+1}-a+1 \right ) } \right \} \]