ODE
\[ x y''(x)+x y'(x)^2=y'(x) \] ODE Classification
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0149203 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \log \left (2 c_1+x^2\right )+c_2\right \}\right \}\]
Maple ✓
cpu = 0.214 (sec), leaf count = 15
\[ \left \{ {\it \_C1}\,{x}^{2}-{\it \_C2}+{{\rm e}^{y \left ( x \right ) }}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x]^2 + x*y''[x] == y'[x],y[x],x]
Mathematica raw output
{{y[x] -> C[2] + Log[x^2 + 2*C[1]]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+x*diff(y(x),x)^2 = diff(y(x),x), y(x),'implicit')
Maple raw output
_C1*x^2-_C2+exp(y(x)) = 0