88.21.4 problem 4

Internal problem ID [24154]
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 : 4
Date solved : Thursday, October 02, 2025 at 10:00:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 28

ode=x^2*D[y[x],{x,2}]+x^2*D[y[x],{x,1}]-x*y[x]==0; 
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} \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),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False