Internal problem ID [14182]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )}=0} \]
✓ Solution by Maple
Time used: 10.859 (sec). Leaf size: 22
dsolve(diff(y(t),t)=(1+2*exp(y(t)))/(exp(y(t))*t*ln(t)),y(t), singsol=all)
\[ y \left (t \right ) = -\ln \left (2\right )-\ln \left (\frac {1}{\ln \left (t \right )^{2} c_{1} -1}\right ) \]
✓ Solution by Mathematica
Time used: 0.685 (sec). Leaf size: 51
DSolve[y'[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*}