43.3.5 problem 1(e)

Internal problem ID [8891]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 05:59:38 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {1}{2} e^{-x^2} \left (x^2+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.148 (sec). Leaf size: 14

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

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