74.8.4 problem 4

Internal problem ID [16140]
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 : Tuesday, January 28, 2025 at 08:51:48 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

\[ y = -\frac {3 \ln \left (2\right )}{8}-\frac {\ln \left (-\ln \left (t \right )-c_{1} \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.313 (sec). Leaf size: 17

DSolve[D[y[t],t]==Exp[8*y[t]]/t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {1}{8} \log (-8 (\log (t)+c_1)) \]