14.4.1 problem 1

Internal problem ID [2519]
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 : 1
Date solved : Monday, January 27, 2025 at 05:58:23 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 t \left (1+y\right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

dsolve([diff(y(t),t)=2*t*(y(t)+1),y(0) = 0],y(t), singsol=all)
 

\[ y = -1+{\mathrm e}^{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 12

DSolve[{D[y[t],t]==2*t*(y[t]+1),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t^2}-1 \]