74.4.49 problem 49

Internal problem ID [15942]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 49
Date solved : Tuesday, January 28, 2025 at 08:24:01 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\mathrm e} \end{align*}

✓ Solution by Maple

Time used: 0.111 (sec). Leaf size: 12

dsolve([diff(y(x),x)=y(x)/ln(y(x)),y(0) = exp(1)],y(x), singsol=all)
 

\[ y = {\mathrm e}^{\sqrt {2 x +1}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 16

DSolve[{D[y[x],x]==y[x]/Log[y[x]],{y[0]==Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\sqrt {2 x+1}} \]