14.2.2 problem 2

Internal problem ID [2490]
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 : 2
Date solved : Sunday, March 30, 2025 at 12:03:13 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(t),t) = (t+1)*(1+y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -1+{\mathrm e}^{\frac {t \left (2+t \right )}{2}} c_1 \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 25

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

\begin{align*} y(t)\to -1+c_1 e^{\frac {1}{2} t (t+2)} \\ y(t)\to -1 \\ \end{align*}

✓ Sympy. Time used: 0.315 (sec). Leaf size: 14

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

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