29.15.7 problem 415

Internal problem ID [5013]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 415
Date solved : Tuesday, March 04, 2025 at 07:43:15 PM
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: 0.002 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.114 (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]
 

\[ y(x)\to \frac {e^x (x-1)+c_1}{e^x-x} \]

✓ Sympy. Time used: 0.362 (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)
 

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