2.536   ODE No. 536

\[ b x \left (x^2-a^2\right ) y'(x)^2+\left (x^2-a^2\right ) y'(x)^3+b x+y'(x)=0 \] Mathematica : cpu = 0.0117279 (sec), leaf count = 64


\[\left \{\left \{y(x)\to -\frac {b x^2}{2}+c_1\right \},\left \{y(x)\to -\tan ^{-1}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1\right \},\left \{y(x)\to \tan ^{-1}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1\right \}\right \}\] Maple : cpu = 0.043 (sec), leaf count = 52


\[y \relax (x ) = -\frac {b \,x^{2}}{2}+c_{1}\]