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 = 0.111509 (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 = 0.053 (sec), leaf count = 41

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