68.1.8 problem Problem 1.6(b)

Internal problem ID [14137]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS. Problems page 28
Problem number : Problem 1.6(b)
Date solved : Tuesday, January 28, 2025 at 06:15:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.710 (sec). Leaf size: 54

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

\begin{align*} y(x)\to \frac {e^{-x-1} \left (\int _1^xe^{K[1]+1} c_1 K[1]dK[1]+c_2\right )}{x} \\ y(x)\to \frac {c_2 e^{-x-1}}{x} \\ \end{align*}