68.6.44 problem 50

Internal problem ID [17354]
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 : Thursday, October 02, 2025 at 02:10:16 PM
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*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 30

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

\[ t +\frac {\left (-y^{2}+2 y-2\right ) {\mathrm e}^{y}-c_1}{y^{2}} = 0 \]

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 32

ode=y[t]+(2*t-y[t]*Exp[y[t]])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.552 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((2*t - y(t)*exp(y(t)))*Derivative(y(t), t) + y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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