88.21.8 problem 8

Internal problem ID [24158]
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 5. Special Techniques for Linear Equations. Exercises at page 149
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:00:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=2 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 29

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x*Derivative(y(x), (x, 2)) + y(x) + 2)/x