68.8.4 problem 4

Internal problem ID [17427]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 4
Date solved : Thursday, October 02, 2025 at 02:20:41 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(y(t),t) = exp(8*y(t))/t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {3 \ln \left (2\right )}{8}-\frac {\ln \left (-\ln \left (t \right )-c_1 \right )}{8} \]

✓ Mathematica. Time used: 0.184 (sec). Leaf size: 17

ode=D[y[t],t]==Exp[8*y[t]]/t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {1}{8} \log (-8 (\log (t)+c_1)) \end{align*}

✓ Sympy. Time used: 5.867 (sec). Leaf size: 189

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - exp(8*y(t))/t,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \log {\left (- \sqrt [8]{- \frac {1}{C_{1} + 8 \log {\left (t \right )}}} \right )}, \ y{\left (t \right )} = \frac {\log {\left (- \frac {1}{C_{1} + 8 \log {\left (t \right )}} \right )}}{8}, \ y{\left (t \right )} = \log {\left (- i \sqrt [8]{- \frac {1}{C_{1} + 8 \log {\left (t \right )}}} \right )}, \ y{\left (t \right )} = \log {\left (i \sqrt [8]{- \frac {1}{C_{1} + 8 \log {\left (t \right )}}} \right )}, \ y{\left (t \right )} = \log {\left (\sqrt [8]{2} \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (- \frac {1}{2} - \frac {i}{2}\right ) \right )}, \ y{\left (t \right )} = \log {\left (\sqrt [8]{2} i \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}, \ y{\left (t \right )} = \log {\left (- \sqrt [8]{2} i \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}, \ y{\left (t \right )} = \log {\left (\sqrt [8]{2} \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}\right ] \]