38.1.29 problem 31

Internal problem ID [8190]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 31
Date solved : Tuesday, September 30, 2025 at 05:18:32 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 9

ode:=x*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

ode=x*D[y[x],x]-2*y[x]==0; 
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)
 

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