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 : Monday, January 27, 2025 at 04:58:54 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x] == x*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

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