ODE
\[ y'(x)^n+x y'(x)-y(x)=0 \] ODE Classification
[_Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.0163097 (sec), leaf count = 14
\[\left \{\left \{y(x)\to c_1^n+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 34
\[ \left \{ \left ( n-1 \right ) \left ( \left ( -{\frac {x}{n}} \right ) ^{ \left ( n-1 \right ) ^{-1}} \right ) ^{n}+y \left ( x \right ) =0,y \left ( x \right ) ={{\it \_C1}}^{n}+{\it \_C1}\,x \right \} \] Mathematica raw input
DSolve[-y[x] + x*y'[x] + y'[x]^n == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + C[1]^n}}
Maple raw input
dsolve(diff(y(x),x)^n+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
(n-1)*((-x/n)^(1/(n-1)))^n+y(x) = 0, y(x) = _C1^n+_C1*x