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 = 0.305495 (sec), leaf count = 48
\[\text {Solve}\left [\left \{n x K[1]=x^{n-1} K[1]^n+y(x),x=c_1 (-((n-1) K[1]))^{\frac {n}{1-n}}\right \},\{y(x),K[1]\}\right ]\]
Maple ✓
cpu = 3.411 (sec), leaf count = 29
\[\left [y \left (x \right ) = \textit {\_C1} \left (\frac {x}{\textit {\_C1}}\right )^{\frac {1}{n}} n -\frac {\left (\frac {1}{\textit {\_C1}}\right )^{-n}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[y[x] - n*x*y'[x] + x^(-1 + n)*y'[x]^n == 0,y[x],x]
Mathematica raw output
Solve[{n*x*K[1] == x^(-1 + n)*K[1]^n + y[x], x == C[1]*(-((-1 + n)*K[1]))^(n/(1 - n))}, {y[x], K[1]}]
Maple raw input
dsolve(x^(n-1)*diff(y(x),x)^n-n*x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x/_C1)^(1/n)*n-1/_C1*(1/_C1)^(-n)]