24.1.11 problem 2(e)

Internal problem ID [4200]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 2(e)
Date solved : Monday, January 27, 2025 at 08:41:56 AM
CAS classification : [_linear]

\begin{align*} \left (x^{3}+x \right ) y^{\prime }+y&=x \end{align*}

✓ Solution by Maple

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

dsolve((x^3+x)*diff(y(x),x)+y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 23

DSolve[(x^3+x)*D[y[x],x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

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