14.2.4 problem 4

Internal problem ID [2492]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 4
Date solved : Sunday, March 30, 2025 at 12:03:19 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{t +y+3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

ode:=diff(y(t),t) = exp(3+t+y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -3-\ln \left (-{\mathrm e}^{t}-c_1 \right ) \]

✓ Mathematica. Time used: 0.898 (sec). Leaf size: 20

ode=D[y[t],t]==Exp[t+y[t]+3]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\log \left (-e^{t+3}-c_1\right ) \]

✓ Sympy. Time used: 0.213 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-exp(t + y(t) + 3) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \log {\left (- \frac {1}{C_{1} + e^{t + 3}} \right )} \]