#### 2.467   ODE No. 467

$y(x) y'(x)^2-4 x y'(x)+y(x)=0$ Mathematica : cpu = 0.262129 (sec), leaf count = 226

$\left \{\left \{y(x)\to \sqrt {x^2+\frac {2\ 2^{2/3} x^4}{\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-48 c_1{}^9 x^3+768 c_1{}^6 x^6-4096 c_1{}^3 x^9+c_1{}^{12}}-c_1{}^6}}+\frac {2^{2/3} c_1{}^3 x}{\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-48 c_1{}^9 x^3+768 c_1{}^6 x^6-4096 c_1{}^3 x^9+c_1{}^{12}}-c_1{}^6}}+\frac {\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-48 c_1{}^9 x^3+768 c_1{}^6 x^6-4096 c_1{}^3 x^9+c_1{}^{12}}-c_1{}^6}}{2\ 2^{2/3}}}\right \}\right \}$ Maple : cpu = 0.135 (sec), leaf count = 148

$\left \{ -{\frac {{\it \_C1}\,x}{y \left ( x \right ) }{\frac {1}{\sqrt [3]{{\frac {1}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( 8\,{x}^{2}-4\, \left ( y \left ( x \right ) \right ) ^{2}-4\,x\sqrt {4\,{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}}}{\frac {1}{\sqrt [3]{{\frac {1}{y \left ( x \right ) } \left ( 2\,x-\sqrt {4\,{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}}}}+x=0,-{\frac {{\it \_C1}\,x}{y \left ( x \right ) }{\frac {1}{\sqrt [3]{{\frac {1}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( x\sqrt {4\,{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}+2\,{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}{\frac {1}{\sqrt [3]{{\frac {1}{y \left ( x \right ) } \left ( 2\,x+\sqrt {4\,{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}}}}+x=0 \right \}$