51.4.8 problem 8

Internal problem ID [10365]
Book : First order enumerated odes
Section : section 4. First order odes solved using series method
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 07:22:37 PM
CAS classification : [_linear]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 26

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

\[ y = \frac {c_1 \left (1+\operatorname {O}\left (x^{6}\right )\right ) x^{2}+\left (-\frac {1}{2}+\operatorname {O}\left (x^{9}\right )\right )}{x^{3}} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 17

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

\[ y(x)\to -\frac {1}{2 x^3}+\frac {c_1}{x} \]

✗ Sympy

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

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