74.8.4 problem 4
Internal
problem
ID
[16069]
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
:
Monday, March 31, 2025 at 02:38:38 PM
CAS
classification
:
[_separable]
\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \end{align*}
✓ Maple. Time used: 0.004 (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: 0.313 (sec). Leaf size: 17
ode=D[y[t],t]==Exp[8*y[t]]/t;
ic={};
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
\[
y(t)\to -\frac {1}{8} \log (-8 (\log (t)+c_1))
\]
✓ Sympy. Time used: 7.973 (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)
\[
\left [ y{\left (t \right )} = \log {\left (- \sqrt [8]{- \frac {1}{C_{1} + 8 \log {\left (t \right )}}} \right )}, \ y{\left (t \right )} = \frac {\log {\left (- \frac {1}{C_{1} + 8 \log {\left (t \right )}} \right )}}{8}, \ y{\left (t \right )} = \log {\left (- i \sqrt [8]{- \frac {1}{C_{1} + 8 \log {\left (t \right )}}} \right )}, \ y{\left (t \right )} = \log {\left (i \sqrt [8]{- \frac {1}{C_{1} + 8 \log {\left (t \right )}}} \right )}, \ y{\left (t \right )} = \log {\left (\sqrt [8]{2} \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (- \frac {1}{2} - \frac {i}{2}\right ) \right )}, \ y{\left (t \right )} = \log {\left (\sqrt [8]{2} i \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}, \ y{\left (t \right )} = \log {\left (- \sqrt [8]{2} i \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}, \ y{\left (t \right )} = \log {\left (\sqrt [8]{2} \sqrt [8]{- \frac {1}{C_{1} + \log {\left (t \right )}}} \left (\frac {1}{2} + \frac {i}{2}\right ) \right )}\right ]
\]