7.2.10 problem 12

Internal problem ID [28]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 12
Date solved : Friday, February 07, 2025 at 08:12:10 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(y(x),x)=x*ln(y(x)),y(1) = 1],y(x), singsol=all)
 

\[ y = 1 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

DSolve[{D[y[x],x]==x*Log[y[x]],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 1 \]