2.418   ODE No. 418

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

✓ Mathematica : cpu = 1.20987 (sec), leaf count = 168

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

\[\left \{\text {Solve}\left [\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}-4 a}-\sqrt {\frac {y(x)}{x}}}+\tanh ^{-1}\left (\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}}}\right )=\frac {\log (x)}{2}+c_1,y(x)\right ],\text {Solve}\left [\tanh ^{-1}\left (\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}}}\right )-\frac {\sqrt {\frac {y(x)}{x}-4 a}}{\sqrt {\frac {y(x)}{x}-4 a}+\sqrt {\frac {y(x)}{x}}}=-\frac {\log (x)}{2}+c_1,y(x)\right ]\right \}\]

✓ Maple : cpu = 0.049 (sec), leaf count = 42

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

\[y \left (x \right ) = 0\]