29.3.8 problem 8

Internal problem ID [7247]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 04:26:11 PM
CAS classification : [_linear]

\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = \frac {\ln \left (x \right )}{2}+\frac {c_1}{\ln \left (x \right )} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 19

ode=(x*Log[x])*D[y[x],x]+y[x]==Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\log (x)}{2}+\frac {c_1}{\log (x)} \end{align*}

✓ Sympy. Time used: 0.206 (sec). Leaf size: 12

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

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