81.4.13 problem 5-14

Internal problem ID [21527]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-14
Date solved : Thursday, October 02, 2025 at 07:46:51 PM
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: 0.015 (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: 0.060 (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)
 

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