3.143   ODE No. 143

\[ \boxed { {x}^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a \left ( y \left ( x \right ) \right ) ^{2} \right ) -b=0} \]

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

Mathematica: cpu = 0.008501 (sec), leaf count = 51 \[ \left \{\left \{y(x)\to -\frac {\sqrt {4 a b+1} \left (\frac {2 c_1}{x^{\sqrt {4 a b+1}}+c_1}-1\right )-1}{2 a x}\right \}\right \} \]

Maple: cpu = 0.032 (sec), leaf count = 49 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,ax} \left ( -\tanh \left ( -{ \frac {\ln \left ( x \right ) }{2}\sqrt {4\,ab+1}}+{\frac {{\it \_C1}}{ 2}\sqrt {4\,ab+1}} \right ) \sqrt {4\,ab+1}+1 \right ) } \right \} \]