1.13.18 problem 18

Internal problem ID [417]
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 : 18
Date solved : Tuesday, September 30, 2025 at 03:58:32 AM
CAS classification : [_separable]

\begin{align*} x^{3} y^{\prime }&=2 y \end{align*}

Using series method with expansion around

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

✗ Maple

Order:=6; 
ode:=x^3*diff(y(x),x) = 2*y(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 13

ode=x^3*D[y[x],x]==2*y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 e^{-\frac {1}{x^2}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

ValueError : ODE x**3*Derivative(y(x), x) - 2*y(x) does not match hint 1st_power_series