14.4.7 problem 7

Internal problem ID [2525]
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 : 7
Date solved : Monday, January 27, 2025 at 05:59:04 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \end{align*}

With initial conditions

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

✗ Solution by Maple

dsolve([diff(y(t),t)=exp(-t^2)+y(t)^2,y(0) = 0],y(t), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[t],t]==Exp[-t^2]+y[t]^2,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

Not solved