6.7.3 problem 3

Internal problem ID [1713]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 05:16:28 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 7

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

\[ y = c_1 x \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to c_1 x\\ y(x)&\to 0 \end{align*}

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

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)
 

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