Internal problem ID [8889]
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: 0.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {x^{-1+n} {y^{\prime }}^{n}-n x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 40
dsolve(x^(n-1)*diff(y(x),x)^n-n*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -x^{n -1} \left (\frac {c_{1} \left (\frac {x}{c_{1}}\right )^{\frac {1}{n}}}{x}\right )^{n}+n c_{1} \left (\frac {x}{c_{1}}\right )^{\frac {1}{n}} \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 54
DSolve[y[x] - n*x*y'[x] + x^(-1 + n)*y'[x]^n==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{y(x)=\frac {n x^2 K[1]-x^n K[1]^n}{x},x=c_1 (K[1]-n K[1])^{\frac {n}{1-n}}\right \},\{y(x),K[1]\}\right ] \]