63.4.31 problem 28

Internal problem ID [13074]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 04:51:26 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.111 (sec). Leaf size: 16

dsolve([diff(y(t),t)=-y(t)^2*exp(-t^2),y(0) = 1/2],y(t), singsol=all)
 

\[ y = \frac {2}{4+\sqrt {\pi }\, \operatorname {erf}\left (t \right )} \]

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 19

DSolve[{D[y[t],t]==-y[t]^2*Exp[-t^2],{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2}{\sqrt {\pi } \text {erf}(t)+4} \]