2.469   ODE No. 469

\[ a x y'(x)+b y(x)+y(x) y'(x)^2=0 \]

✓ Mathematica : cpu = 0.217318 (sec), leaf count = 157

DSolve[b*y[x] + a*x*Derivative[1][y][x] + y[x]*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\text {Solve}\left [\frac {a \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a\right )+(a+2 b) \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a-2 b\right )}{4 (a+b)}=-\frac {\log (x)}{2}+c_1,y(x)\right ],\text {Solve}\left [\frac {a \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a\right )+(a+2 b) \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+2 b\right )}{4 (a+b)}=-\frac {\log (x)}{2}+c_1,y(x)\right ]\right \}\]

✓ Maple : cpu = 0.311 (sec), leaf count = 264

dsolve(y(x)*diff(y(x),x)^2+a*x*diff(y(x),x)+b*y(x) = 0,y(x))
 

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