23.1.428 problem 418

Internal problem ID [5035]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 418
Date solved : Tuesday, September 30, 2025 at 11:28:20 AM
CAS classification : [_linear]

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

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

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

\[ y = \frac {\left (-1+x \right ) {\mathrm e}^{x}+c_1}{-x +{\mathrm e}^{x}} \]

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.229 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1} - x e^{x} + e^{x}}{x - e^{x}} \]