7.13.16 problem 16

Internal problem ID [415]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.1 (Introduction). Problems at page 206
Problem number : 16
Date solved : Saturday, March 29, 2025 at 04:53:08 PM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 14

Order:=6; 
ode:=2*x*diff(y(x),x) = y(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 \sqrt {x}+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 11

ode=2*x*D[y[x],x]==y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \sqrt {x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

ValueError : ODE 2*x*Derivative(y(x), x) - y(x) does not match hint 1st_power_series