12.2.4 problem 4

Internal problem ID [1540]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 4
Date solved : Saturday, March 29, 2025 at 10:58:11 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=x*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1}{x^{3}} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 16

ode=x*D[y[x],x] +3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {c_1}{x^3} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{3}} \]