\[ \boxed { a{x}^{n}f \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) =0} \]
Mathematica: cpu = 0.102013 (sec), leaf count = 114 \[ \text {Solve}\left [\left \{y(x)=a f(\text {K$\$$1487621}) x^n+\text {K$\$$1487621} x,x=\left (n f(\text {K$\$$1487621})^{\frac {1}{n}-1} \left (\int _1^{\text {K$\$$1487621}} -\frac {f(K[1])^{\frac {n-1}{n}-1}}{a n} \, dK[1]\right )-f(\text {K$\$$1487621})^{\frac {1}{n}-1} \left (\int _1^{\text {K$\$$1487621}} -\frac {f(K[1])^{\frac {n-1}{n}-1}}{a n} \, dK[1]\right )+c_1 f(\text {K$\$$1487621})^{\frac {1}{n}-1}\right ){}^{\frac {1}{n-1}}\right \},\{y(x),\text {K$\$$1487621}\}\right ] \]
Maple: cpu = 0.203 (sec), leaf count = 199 \[ \left \{ [y \left ( {\it \_T} \right ) =a \left ( \left ( -{\frac {1}{af \left ( {\it \_T} \right ) n} \left ( -{\it \_C1}\,an+\int \! \left ( f \left ( {\it \_T} \right ) \right ) ^{-{n}^{-1}}\,{\rm d}{\it \_T}n- \int \! \left ( f \left ( {\it \_T} \right ) \right ) ^{-{n}^{-1}} \,{\rm d}{\it \_T} \right ) } \right ) ^{ \left ( n-1 \right ) ^{-1}} \left ( f \left ( {\it \_T} \right ) \right ) ^{{\frac {1}{n \left ( n-1 \right ) }}} \right ) ^{n}f \left ( {\it \_T} \right ) +{\it \_T}\, \left ( -{\frac {1}{af \left ( {\it \_T} \right ) n} \left ( -{\it \_C1} \,an+\int \! \left ( f \left ( {\it \_T} \right ) \right ) ^{-{n}^{-1}} \,{\rm d}{\it \_T}n-\int \! \left ( f \left ( {\it \_T} \right ) \right ) ^{-{n}^{-1}}\,{\rm d}{\it \_T} \right ) } \right ) ^{ \left ( n- 1 \right ) ^{-1}} \left ( f \left ( {\it \_T} \right ) \right ) ^{{\frac { 1}{n \left ( n-1 \right ) }}},x \left ( {\it \_T} \right ) = \left ( -{ \frac {1}{af \left ( {\it \_T} \right ) n} \left ( -{\it \_C1}\,an+\int \! \left ( f \left ( {\it \_T} \right ) \right ) ^{-{n}^{-1}}\,{\rm d}{ \it \_T}n-\int \! \left ( f \left ( {\it \_T} \right ) \right ) ^{-{n}^{- 1}}\,{\rm d}{\it \_T} \right ) } \right ) ^{ \left ( n-1 \right ) ^{-1}} \left ( f \left ( {\it \_T} \right ) \right ) ^{{\frac {1}{n \left ( n-1 \right ) }}}] \right \} \]