68.2.11 problem 16

Internal problem ID [17139]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 16
Date solved : Thursday, October 02, 2025 at 01:44:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = -\frac {{\mathrm e}^{-x^{2}}}{2}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

ode=D[y[x],x]==x*Exp[-x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{-x^2}}{2}+c_1 \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} - \frac {e^{- x^{2}}}{2} \]