65.3.5 problem 8.1 (v)

Internal problem ID [13723]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 8, Separable equations. Exercises page 72
Problem number : 8.1 (v)
Date solved : Tuesday, January 28, 2025 at 05:59:47 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(t),t)=exp(-t^2)*y(t)^2,y(t), singsol=all)
 

\[ y = -\frac {2}{\sqrt {\pi }\, \operatorname {erf}\left (t \right )-2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 27

DSolve[D[y[t],t]==Exp[-t^2]*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\frac {2}{\sqrt {\pi } \text {erf}(t)+2 c_1} \\ y(t)\to 0 \\ \end{align*}