14.4.17 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 : Monday, January 27, 2025 at 05:59:28 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*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 5

dsolve([diff(y(t),t)=t*(1+y(t)),y(0) = -1],y(t), singsol=all)
 

\[ y = -1 \]

✓ Solution by Mathematica

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

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

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