29.3.3 problem 3

Internal problem ID [7242]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 04:26:09 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=diff(y(x),x)+2*x*y(x)-x*exp(-x^2) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 24

ode=D[y[x],x]+2*x*y[x]-x*Exp[-x^2]==0; 
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: 0.152 (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)
 

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