20.2.4 problem Problem 4

Internal problem ID [3596]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations. page 43
Problem number : Problem 4
Date solved : Monday, January 27, 2025 at 07:47:02 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 8

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

\[ y \left (x \right ) = \ln \left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 15

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

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