65.3.5 problem 8.1 (v)

Internal problem ID [13644]
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 : Wednesday, March 05, 2025 at 10:06:16 PM
CAS classification : [_separable]

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

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

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

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

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

ode=D[y[t],t]==Exp[-t^2]*y[t]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**2*exp(-t**2) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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