2.573   ODE No. 573

\[ f\left (x y'(x)^2\right )+2 x y'(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.0200109 (sec), leaf count = 42

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

\[\left \{\left \{y(x)\to f(c_1)-2 \sqrt {c_1} \sqrt {x},y(x)\to f(c_1)+2 \sqrt {c_1} \sqrt {x}\right \}\right \}\]

✓ Maple : cpu = 0.102 (sec), leaf count = 24

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

\[y \left (x \right ) = c_{1} +2 \sqrt {x}\, \operatorname {RootOf}\left (-f \left (\textit {\_Z}^{2}\right )-2 \textit {\_Z} +c_{1} +c_{2} \right )\]