Internal problem ID [8134]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 554.
ODE order: 1.
ODE degree: 553.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x^{-1+n} \left (y^{\prime }\right )^{n}-n x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 1.102 (sec). Leaf size: 29
dsolve(x^(n-1)*diff(y(x),x)^n-n*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} n \left (\frac {x}{c_{1}}\right )^{\frac {1}{n}}-\frac {\left (\frac {1}{c_{1}}\right )^{-n}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 54
DSolve[y[x] - n*x*y'[x] + x^(-1 + n)*y'[x]^n==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{y(x)=\frac {n x^2 K[1]-x^n K[1]^n}{x},x=c_1 (K[1]-n K[1])^{\frac {n}{1-n}}\right \},\{y(x),K[1]\}\right ] \]