71.2.7 problem 7

Internal problem ID [14268]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 7
Date solved : Monday, March 31, 2025 at 12:14:52 PM
CAS classification : [_separable]

\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=x*ln(x)*diff(y(x),x)-(ln(x)+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 x \ln \left (x \right ) \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 17

ode=(x*Log[x])*D[y[x],x]-(1+Log[x])*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to e c_1 x \log (x) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.243 (sec). Leaf size: 8

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

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