Internal problem ID [3539]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 283.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }+y x=x} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.034 (sec). Leaf size: 24
DSolve[(1-x^2)y'[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*}