60.1.154 problem 155

Internal problem ID [10168]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 155
Date solved : Monday, January 27, 2025 at 06:31:00 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 36

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

\begin{align*} y(x)\to x+\frac {1}{-\int _1^x\frac {1}{1-K[1]^2}dK[1]+c_1} \\ y(x)\to x \\ \end{align*}