29.10.16 problem 282

Internal problem ID [4882]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 282
Date solved : Monday, January 27, 2025 at 09:46:19 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 46

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

\[ y \left (x \right ) = \frac {a \ln \left (x +\sqrt {x^{2}-1}\right ) \sqrt {x^{2}-1}}{\left (x -1\right ) \left (x +1\right )}+\frac {c_{1}}{\sqrt {x -1}\, \sqrt {x +1}} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 32

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

\[ y(x)\to \frac {a \log \left (\sqrt {x^2-1}+x\right )+c_1}{\sqrt {x^2-1}} \]