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 : Monday, January 27, 2025 at 05:54:12 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

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

DSolve[D[y[t],t]==(1+t)*(1+y[t]),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*}