Internal problem ID [14947]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 1. Basic concepts and definitions. Exercises page 18
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }+y x=2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((1-x^2)*diff(y(x),x)+x*y(x)=2*x,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {-1+x}\, \sqrt {1+x}\, c_{1} +2 \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 24
DSolve[(1-x^2)*y'[x]+x*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2+c_1 \sqrt {x^2-1} \\ y(x)\to 2 \\ \end{align*}