89.7.23 problem 22 (n=1,k=0)

Internal problem ID [24454]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 22 (n=1,k=0)
Date solved : Thursday, October 02, 2025 at 10:36:59 PM
CAS classification : [_separable]

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

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

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

\[ y = c_1 \,x^{2} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to c_1 x^2\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{2} \]