68.1.8 problem Problem 1.6(b)

Internal problem ID [14066]
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 : Monday, March 31, 2025 at 12:02:30 PM
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*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

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

\[ y = \frac {c_1 \left (-1+x \right )+c_2 \,{\mathrm e}^{-x}}{x} \]

✓ Mathematica. Time used: 0.71 (sec). Leaf size: 54

ode=x^2*D[y[x],{x,2}]+x*(1+x)*D[y[x],x]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 1.067 (sec). Leaf size: 388

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(x + 1)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]