60.1.155 problem 156

Internal problem ID [10169]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 156
Date solved : Monday, January 27, 2025 at 06:31:03 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

\[ y = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1} +x} \]

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 26

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

\begin{align*} y(x)\to \frac {1}{x+c_1 \sqrt {x^2-1}} \\ y(x)\to 0 \\ \end{align*}