12.1.8 problem 3(c)

Internal problem ID [1526]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 3(c)
Date solved : Tuesday, March 04, 2025 at 12:38:07 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \frac {\ln \left (x \right ) x^{2}}{2}-\frac {x^{2}}{4}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 24

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

\[ y(x)\to -\frac {x^2}{4}+\frac {1}{2} x^2 \log (x)+c_1 \]

✓ Sympy. Time used: 0.145 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} + \frac {x^{2} \log {\left (x \right )}}{2} - \frac {x^{2}}{4} \]