ODE
\[ -(x+1) y'(x)+y'(x) \log \left (y'(x)\right )+y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.00210199 (sec), leaf count = 16
\[\left \{\left \{y(x)\to c_1 \left (-\log \left (c_1\right )+x+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.038 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) -{{\rm e}^{x}}=0,y \left ( x \right ) ={\it \_C1}\, \left ( -\ln \left ( {\it \_C1} \right ) +x+1 \right ) \right \} \] Mathematica raw input
DSolve[y[x] - (1 + x)*y'[x] + Log[y'[x]]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(1 + x - Log[C[1]])}}
Maple raw input
dsolve(diff(y(x),x)*ln(diff(y(x),x))-(1+x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x)-exp(x) = 0, y(x) = _C1*(-ln(_C1)+x+1)