67.2.60 problem Problem 20(g)

Internal problem ID [13946]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 20(g)
Date solved : Monday, March 31, 2025 at 08:20:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+(x-1)/x*diff(y(x),x)+y(x)/x^3 = 1/x^3*exp(-1/x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+(x-1)/x*D[y[x],x]+y[x]/x^3==1/x^3*Exp[-1/x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + (x - 1)*Derivative(y(x), x)/x + y(x)/x**3 - exp(-1/x)/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3*exp(1/x)*Derivative(y(x), (x, 2)) - y(x)*exp(1/x) + 1)*exp(-1/x)/(x**2*(x - 1)) cannot be solved by the factorable group method