8.3.1 problem 1

Internal problem ID [677]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 11:31:50 AM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 20

ode=2*x*y[x]+D[y[x],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: 0.240 (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)
 

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