19.1.7 problem 7

Internal problem ID [4219]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 07:07:35 AM
CAS classification : [_separable]

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

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

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

\[ y = c_1 x \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 14

ode=x*D[y[x],x]==y[x]; 
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)
 

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