44.5.69 problem 58 (a 1)

Internal problem ID [7131]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 58 (a 1)
Date solved : Tuesday, February 04, 2025 at 12:28:49 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

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

\[ y = {\mathrm e}^{x -{\mathrm e}} \ln \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 15

DSolve[{D[y[x],x]==y[x]+y[x]/(x*Log[x]),{y[Exp[1]]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x-e} \log (x) \]