30.3.5 problem 5

Internal problem ID [7461]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 04:36:30 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 22

ode=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^{-\frac {x^2}{2}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 10

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

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