60.1.264 problem 265

Internal problem ID [10278]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 265
Date solved : Monday, January 27, 2025 at 06:43:28 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x^{n \left (n +1\right )} y-1\right ) y^{\prime }+2 \left (n +1\right )^{2} x^{n -1} \left (x^{n^{2}} y^{2}-1\right )&=0 \end{align*}

✗ Solution by Maple

dsolve((x^(n*(n+1))*y(x)-1)*diff(y(x),x)+2*(n+1)^2*x^(n-1)*(x^(n^2)*y(x)^2-1)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(x^(n*(n+1))*y[x]-1)*D[y[x],x]+2*(n+1)^2*x^(n-1)*(x^(n^2)*y[x]^2-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved