ODE No. 467

\[ y(x) y'(x)^2-4 x y'(x)+y(x)=0 \] Mathematica : cpu = 0.243314 (sec), leaf count = 226

DSolve[y[x] - 4*x*Derivative[1][y][x] + y[x]*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \sqrt {x^2+\frac {2^{2/3} c_1{}^3 x}{\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-4096 c_1{}^3 x^9+768 c_1{}^6 x^6-48 c_1{}^9 x^3+c_1{}^{12}}-c_1{}^6}}+\frac {\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-4096 c_1{}^3 x^9+768 c_1{}^6 x^6-48 c_1{}^9 x^3+c_1{}^{12}}-c_1{}^6}}{2\ 2^{2/3}}+\frac {2\ 2^{2/3} x^4}{\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-4096 c_1{}^3 x^9+768 c_1{}^6 x^6-48 c_1{}^9 x^3+c_1{}^{12}}-c_1{}^6}}}\right \}\right \}\] Maple : cpu = 0.075 (sec), leaf count = 148

dsolve(y(x)*diff(y(x),x)^2-4*x*diff(y(x),x)+y(x) = 0,y(x))
 

\[-\frac {c_{1} x}{y \left (x \right ) \left (\frac {x \sqrt {4 x^{2}-y \left (x \right )^{2}}+2 x^{2}-y \left (x \right )^{2}}{y \left (x \right )^{2}}\right )^{\frac {1}{3}} \left (\frac {2 x +\sqrt {4 x^{2}-y \left (x \right )^{2}}}{y \left (x \right )}\right )^{\frac {1}{3}}}+x = 0\]