68.4.47 problem 47

Internal problem ID [17227]
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 : 47
Date solved : Thursday, October 02, 2025 at 01:59:08 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.090 (sec). Leaf size: 16

ode:=diff(y(t),t) = exp(t)/(y(t)+1); 
ic:=[y(0) = -2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -1-\sqrt {-1+2 \,{\mathrm e}^{t}} \]

✓ Mathematica. Time used: 0.457 (sec). Leaf size: 20

ode=D[y[t],t]==Exp[t]/(y[t]+1); 
ic={y[0]==-2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\sqrt {2 e^t-1}-1 \end{align*}

✓ Sympy. Time used: 0.211 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - exp(t)/(y(t) + 1),0) 
ics = {y(0): -2} 
dsolve(ode,func=y(t),ics=ics)
 

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