68.4.49 problem 49

Internal problem ID [17229]
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 : Thursday, October 02, 2025 at 01:59:13 PM
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*}

✓ Maple. Time used: 0.069 (sec). Leaf size: 12

ode:=diff(y(x),x) = y(x)/ln(y(x)); 
ic:=[y(0) = exp(1)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to e^{\sqrt {2 x+1}} \end{align*}

✓ Sympy. Time used: 0.616 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)/log(y(x)) + Derivative(y(x), x),0) 
ics = {y(0): E} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{\sqrt {2} \sqrt {x + \frac {1}{2}}} \]