81.4.3 problem 5-4

Internal problem ID [21517]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-4
Date solved : Thursday, October 02, 2025 at 07:46:35 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 20

ode=D[y[x],x]+2*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-x^2}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 8

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

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