84.8.4 problem 4.13

Internal problem ID [22116]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Supplementary problems
Problem number : 4.13
Date solved : Thursday, October 02, 2025 at 08:25:23 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 12

ode:=x+1/y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 17

ode=x+1/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}} \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 10

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

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