88.19.4 problem 4

Internal problem ID [24132]
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 139
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:00:05 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x} \ln \left (x \right )}{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 0.184 (sec). Leaf size: 20

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)*log(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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