74.4.24 problem 24

Internal problem ID [15917]
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 : 24
Date solved : Tuesday, January 28, 2025 at 08:21:12 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \end{align*}

✓ Solution by Maple

Time used: 2.525 (sec). Leaf size: 22

dsolve(diff(y(t),t)=(1+2*exp(y(t)))/(exp(y(t))*t*ln(t)),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.709 (sec). Leaf size: 51

DSolve[D[y[t],t]==(1+2*Exp[y[t]])/(Exp[y[t]]*t*Log[t]),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \log \left (\frac {1}{2} \left (-1+e^{2 c_1} \log ^2(t)\right )\right ) \\ y(t)\to -\log (2)-i \pi \\ y(t)\to -\log (2)+i \pi \\ \end{align*}