#### 2.642   ODE No. 642

$y'(x)=\frac {\left (4 a x-y(x)^2\right )^2}{y(x)}$ Mathematica : cpu = 0.16373 (sec), leaf count = 105

$\left \{\left \{y(x)\to -\sqrt {4 a x-\sqrt {2} \sqrt {a} \tanh \left (\frac {2 \sqrt {2} a x-\sqrt {2} c_1}{\sqrt {a}}\right )}\right \},\left \{y(x)\to \sqrt {4 a x-\sqrt {2} \sqrt {a} \tanh \left (\frac {2 \sqrt {2} a x-\sqrt {2} c_1}{\sqrt {a}}\right )}\right \}\right \}$ Maple : cpu = 0.259 (sec), leaf count = 286

$\left \{ y \left ( x \right ) ={\sqrt {4}\sqrt { \left ( {\it \_C1}\, \left ( ax-{\frac {\sqrt {2}}{4}\sqrt {a}} \right ) {{\rm e}^{2\,x \left ( \sqrt {2}\sqrt {a}-2\,ax \right ) }}+{{\rm e}^{-2\,x \left ( \sqrt {2}\sqrt {a}+2\,ax \right ) }} \left ( ax+{\frac {\sqrt {2}}{4}\sqrt {a}} \right ) \right ) \left ( {\it \_C1}\,{{\rm e}^{2\,x \left ( \sqrt {2}\sqrt {a}-2\,ax \right ) }}+{{\rm e}^{-2\,x \left ( \sqrt {2}\sqrt {a}+2\,ax \right ) }} \right ) } \left ( {\it \_C1}\,{{\rm e}^{2\,x \left ( \sqrt {2}\sqrt {a}-2\,ax \right ) }}+{{\rm e}^{-2\,x \left ( \sqrt {2}\sqrt {a}+2\,ax \right ) }} \right ) ^{-1}},y \left ( x \right ) =-{\sqrt {4}\sqrt { \left ( {\it \_C1}\, \left ( ax-{\frac {\sqrt {2}}{4}\sqrt {a}} \right ) {{\rm e}^{2\,x \left ( \sqrt {2}\sqrt {a}-2\,ax \right ) }}+{{\rm e}^{-2\,x \left ( \sqrt {2}\sqrt {a}+2\,ax \right ) }} \left ( ax+{\frac {\sqrt {2}}{4}\sqrt {a}} \right ) \right ) \left ( {\it \_C1}\,{{\rm e}^{2\,x \left ( \sqrt {2}\sqrt {a}-2\,ax \right ) }}+{{\rm e}^{-2\,x \left ( \sqrt {2}\sqrt {a}+2\,ax \right ) }} \right ) } \left ( {\it \_C1}\,{{\rm e}^{2\,x \left ( \sqrt {2}\sqrt {a}-2\,ax \right ) }}+{{\rm e}^{-2\,x \left ( \sqrt {2}\sqrt {a}+2\,ax \right ) }} \right ) ^{-1}} \right \}$