88.10.4 problem 4

Internal problem ID [24039]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 52
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:55:03 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = x -\ln \left (x +2\right )-c_1 \,{\mathrm e}^{-2} \operatorname {Ei}_{1}\left (-x -2\right )+c_2 \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {c_1 \operatorname {ExpIntegralEi}(x+2)}{e^2}+x-\log (x+2)+c_2 \end{align*}

✓ Sympy. Time used: 1.178 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} + \int \frac {C_{2} e^{x} + x + 1}{x + 2}\, dx \]