42.1.21 problem 3.48 (c)

Internal problem ID [6843]
Book : Advanced Mathematical Methods for Scientists and Engineers, Bender and Orszag. Springer October 29, 1999
Section : Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page 136
Problem number : 3.48 (c)
Date solved : Sunday, March 30, 2025 at 11:24:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \end{align*}

Using series method with expansion around

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

✗ Maple

Order:=6; 
ode:=x^3*diff(diff(y(x),x),x)+y(x) = 1/x^4; 
dsolve(ode,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.563 (sec). Leaf size: 873

ode=x^3*D[y[x],{x,2}]+y[x]==1/x^4; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 2)) + y(x) - 1/x**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : ODE x**3*Derivative(y(x), (x, 2)) + y(x) - 1/x**4 does not match hint 2nd_power_series_regular