75.1.14 problem 16

Internal problem ID [16677]
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
Date solved : Tuesday, January 28, 2025 at 09:17:46 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\[ y = \sqrt {x -1}\, \sqrt {x +1}\, c_{1} +2 \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 24

DSolve[(1-x^2)*D[y[x],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*}