43.17.3 problem 1(c)

Internal problem ID [8996]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 4. Linear equations with Regular Singular Points. Page 154
Problem number : 1(c)
Date solved : Tuesday, September 30, 2025 at 06:01:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \end{align*}

Using series method with expansion around

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

✗ Maple

Order:=8; 
ode:=x^2*diff(diff(y(x),x),x)-5*diff(y(x),x)+3*x^2*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 106

ode=x^2*D[y[x],{x,2}]-5*D[y[x],x]+3*x^2*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

\[ y(x)\to c_1 \left (\frac {339 x^7}{8750}+\frac {49 x^6}{1250}+\frac {18 x^5}{625}+\frac {3 x^4}{50}+\frac {x^3}{5}+1\right )+c_2 e^{-5/x} \left (-\frac {302083 x^7}{218750}+\frac {5243 x^6}{6250}-\frac {357 x^5}{625}+\frac {113 x^4}{250}-\frac {49 x^3}{125}+\frac {6 x^2}{25}-\frac {2 x}{5}+1\right ) x^2 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*y(x) + x**2*Derivative(y(x), (x, 2)) - 5*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=8)
 

ValueError : ODE 3*x**2*y(x) + x**2*Derivative(y(x), (x, 2)) - 5*Derivative(y(x), x) does not match hint 2nd_power_series_regular