88.18.4 problem 4

Internal problem ID [24123]
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 133
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:00:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+4*y(x) = exp(2*x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (\ln \left (x \right ) x +x \left (c_1 -1\right )+c_2 \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==Exp[2*x]/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x} (x \log (x)+(-1+c_2) x+c_1) \end{align*}

✓ Sympy. Time used: 0.160 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - exp(2*x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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