13.5.14 problem 17

Internal problem ID [2360]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.10. Page 80
Problem number : 17
Date solved : Tuesday, March 04, 2025 at 02:08:03 PM
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: 0.004 (sec). Leaf size: 5

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

\[ y(t)\to -1 \]

✓ Sympy. Time used: 0.277 (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)
 

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