2.143   ODE No. 143

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

\[ x^2 \left (a y(x)^2+y'(x)\right )-b=0 \] Mathematica : cpu = 0.0896426 (sec), leaf count = 51

\[\left \{\left \{y(x)\to -\frac {-1+\sqrt {4 a b+1} \left (-1+\frac {2 c_1}{x^{\sqrt {4 a b+1}}+c_1}\right )}{2 a x}\right \}\right \}\] Maple : cpu = 0.046 (sec), leaf count = 41

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