29.10.17 problem 283

Internal problem ID [4883]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 283
Date solved : Monday, January 27, 2025 at 09:46:21 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

\[ y \left (x \right ) = \sqrt {x -1}\, \sqrt {x +1}\, c_{1} +1 \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 24

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

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