60.1.551 problem 554

Internal problem ID [10565]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 554
Date solved : Monday, January 27, 2025 at 09:05:44 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.250 (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)
 

\[ y = -\left (\frac {c_{1} \left (\frac {x}{c_{1}}\right )^{\frac {1}{n}}}{x}\right )^{n} x^{n -1}+n c_{1} \left (\frac {x}{c_{1}}\right )^{\frac {1}{n}} \]

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 54

DSolve[y[x] - n*x*D[y[x],x] + x^(-1 + n)*D[y[x],x]^n==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{y(x)=\frac {n x^2 K[1]-x^n K[1]^n}{x},x=c_1 (K[1]-n K[1])^{\frac {n}{1-n}}\right \},\{y(x),K[1]\}\right ] \]