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*}