8.7 problem 7

Internal problem ID [14409]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

\[ \boxed {y^{\prime }-\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )}=0} \]

Solution by Maple

Time used: 0.063 (sec). Leaf size: 35

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

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

Solution by Mathematica

Time used: 10.553 (sec). Leaf size: 61

DSolve[y'[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*}