8.4.17 problem 17

Internal problem ID [2535]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.10. Existence-uniqueness theorem. Excercises page 80
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 05:46:32 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=t \left (1+y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 5

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

\[ y = -1 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to -1 \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 5

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

\[ y{\left (t \right )} = -1 \]