2.143   ODE No. 143

\[ x^2 \left (a y(x)^2+y'(x)\right )-b=0 \] Mathematica : cpu = 0.0985813 (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


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