85.9.2 problem 1 (b)

Internal problem ID [22476]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 37
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:40:36 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 9

ode:=diff(y(x),x) = -y(x)/x; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {3}{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 10

ode=D[y[x],{x,1}]==-y[x]/x; 
ic={y[1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3}{x} \end{align*}

✓ Sympy. Time used: 0.058 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + y(x)/x,0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3}{x} \]