87.18.3 problem 3

Internal problem ID [23644]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 135
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:43:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = exp(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\ln \left (x \right ) x +x \left (c_1 -1\right )+c_2 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + \log {\left (x \right )}\right )\right ) e^{x} \]