\[ a x^n f\left (y'(x)\right )+x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.163189 (sec), leaf count = 124
\[\text {Solve}\left [\left \{y(x)=a x^n f(K[1])+x K[1],x=\left (n f(K[1])^{\frac {1}{n}-1} \int _1^{K[1]}-\frac {f(K[2])^{\frac {n-1}{n}-1}}{a n}dK[2]-f(K[1])^{\frac {1}{n}-1} \int _1^{K[1]}-\frac {f(K[2])^{\frac {n-1}{n}-1}}{a n}dK[2]+c_1 f(K[1])^{\frac {1}{n}-1}\right ){}^{\frac {1}{n-1}}\right \},\{y(x),K[1]\}\right ]\] ✓ Maple : cpu = 0.517 (sec), leaf count = 169
\[\left \{\left [y \left (\textit {\_T} \right ) = \textit {\_T} \left (\frac {c_{1} a n +\left (-n +1\right ) \left (\int f \left (\textit {\_T} \right )^{-\frac {1}{n}}d \textit {\_T} \right )}{a n f \left (\textit {\_T} \right )}\right )^{\frac {1}{n -1}} f \left (\textit {\_T} \right )^{\frac {1}{\left (n -1\right ) n}}+a \left (\left (\frac {c_{1} a n +\left (-n +1\right ) \left (\int f \left (\textit {\_T} \right )^{-\frac {1}{n}}d \textit {\_T} \right )}{a n f \left (\textit {\_T} \right )}\right )^{\frac {1}{n -1}} f \left (\textit {\_T} \right )^{\frac {1}{\left (n -1\right ) n}}\right )^{n} f \left (\textit {\_T} \right ), x \left (\textit {\_T} \right ) = \left (\frac {c_{1} a n +\left (-n +1\right ) \left (\int f \left (\textit {\_T} \right )^{-\frac {1}{n}}d \textit {\_T} \right )}{a n f \left (\textit {\_T} \right )}\right )^{\frac {1}{n -1}} f \left (\textit {\_T} \right )^{\frac {1}{\left (n -1\right ) n}}\right ]\right \}\]