88.21.10 problem 11

Internal problem ID [24160]
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 : 11
Date solved : Thursday, October 02, 2025 at 10:00:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {c_1}{1-x}-c_2 e^x \end{align*}

✗ Sympy

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

False