74.8.7 problem 7

Internal problem ID [16143]
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 : 7
Date solved : Tuesday, January 28, 2025 at 08:51:54 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.116 (sec). Leaf size: 35

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

\begin{align*} y &= {\mathrm e}^{\sqrt {2 c_{1} -{\mathrm e}^{-2 t}}} \\ y &= {\mathrm e}^{-\sqrt {2 c_{1} -{\mathrm e}^{-2 t}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 11.160 (sec). Leaf size: 61

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

\begin{align*} y(t)\to e^{-e^{-t} \sqrt {-1+2 c_1 e^{2 t}}} \\ y(t)\to e^{e^{-t} \sqrt {-1+2 c_1 e^{2 t}}} \\ y(t)\to 0 \\ \end{align*}