74.6.44 problem 50

Internal problem ID [16067]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 08:35:09 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.210 (sec). Leaf size: 34

dsolve(y(t)+(2*t-y(t)*exp(y(t)))*diff(y(t),t)=0,y(t), singsol=all)
 

\[ \frac {\left (-y^{2}+2 y-2\right ) {\mathrm e}^{y}+t y^{2}-c_{1}}{y^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 32

DSolve[y[t]+(2*t-y[t]*Exp[y[t]])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [t=\frac {e^{y(t)} \left (y(t)^2-2 y(t)+2\right )}{y(t)^2}+\frac {c_1}{y(t)^2},y(t)\right ] \]