74.1.31 problem 38

Internal problem ID [15811]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 08:08:01 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (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]
 

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