29.10.15 problem 281

Internal problem ID [4881]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 281
Date solved : Monday, January 27, 2025 at 09:46:17 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 22

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

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