29.10.14 problem 280

Internal problem ID [4880]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 280
Date solved : Monday, January 27, 2025 at 09:46:16 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 23

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

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