44.2.16 problem 16

Internal problem ID [6948]
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. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 16
Date solved : Sunday, March 30, 2025 at 11:30:34 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=x*D[y[x],x]==2*y[x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 0 \]

✗ Sympy

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

ValueError : Couldnt solve for initial conditions