78.8.19 problem 19

Internal problem ID [18138]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 19
Date solved : Thursday, March 13, 2025 at 11:40:57 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 17

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

\[ y(x)\to e^{-x^2} (x+c_1) \]

✓ Sympy. Time used: 0.209 (sec). Leaf size: 10

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

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