38.3.21 problem 29

Internal problem ID [8288]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 05:21:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = x \left (\operatorname {Ei}_{1}\left (x \right ) c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.269 (sec). Leaf size: 63

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

\begin{align*} y(x)&\to \sqrt {x} \left (c_2 \int _1^x\frac {e^{-K[2]-1}}{K[2]}dK[2]+c_1\right ) \exp \left (\frac {1}{2} \left (-\int _1^x\left (1-\frac {1}{K[1]}\right )dK[1]+x+1\right )\right ) \end{align*}

✗ Sympy

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

False