ODE
\[ x^{n-1} y'(x)^n-n x y'(x)+y(x)=0 \] ODE Classification
[`y=_G(x,y')`]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 0.114474 (sec), leaf count = 44
\[\text {Solve}\left [\left \{\text {K$\$$202459} n x=\text {K$\$$202459}^n x^{n-1}+y(x),x=c_1 (\text {K$\$$202459}-\text {K$\$$202459} n)^{\frac {n}{1-n}}\right \},\{y(x),\text {K$\$$202459}\}\right ]\]
Maple ✓
cpu = 0.472 (sec), leaf count = 63
\[ \left \{ [y \left ( {\it \_T} \right ) =-{\frac {1}{{\it \_C1}} \left ( {\it \_C1}\,{{\it \_T}}^{-{\frac {n}{n-1}}} \right ) ^{n}{{\it \_T}}^{{\frac {{n}^{2}}{n-1}}}}+{\it \_C1}\,n{{\it \_T}}^{- \left ( n-1 \right ) ^{-1}},x \left ( {\it \_T} \right ) ={\it \_C1}\,{{\it \_T}}^{-{\frac {n}{n-1}}}] \right \} \] Mathematica raw input
DSolve[y[x] - n*x*y'[x] + x^(-1 + n)*y'[x]^n == 0,y[x],x]
Mathematica raw output
Solve[{K$202459*n*x == K$202459^n*x^(-1 + n) + y[x], x == (K$202459 - K$202459*n)^(n/(1 - n))*C[1]}, {y[x], K$202459}]
Maple raw input
dsolve(x^(n-1)*diff(y(x),x)^n-n*x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
[y(_T) = -(_C1*_T^(-1/(n-1)*n))^n/_C1*_T^(n^2/(n-1))+_C1*n*_T^(-1/(n-1)), x(_T) = _C1*_T^(-1/(n-1)*n)]