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 = 0.30424 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_2-\log \left (x^2-2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.094 (sec), leaf count = 17
\[\left [y \left (x \right ) = -\ln \left (-\frac {x^{2} \textit {\_C1}}{2}-\textit {\_C2} \right )\right ]\] Mathematica raw input
DSolve[x*y''[x] == y'[x] + x*y'[x]^2,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))
Maple raw output
[y(x) = -ln(-1/2*x^2*_C1-_C2)]