49.16.8 problem 2(c)

Internal problem ID [7706]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 4. Linear equations with Regular Singular Points. Page 149
Problem number : 2(c)
Date solved : Sunday, March 30, 2025 at 12:19:26 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-(2+I)*x*diff(y(x),x)+3*I*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{3}+c_2 \,x^{i} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 20

ode=x^2*D[y[x],{x,2}]-(2+I)*x*D[y[x],x]+3*I*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 x^i+c_2 x^3 \]

✓ Sympy. Time used: 2.565 (sec). Leaf size: 1056

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*complex(-2, -1)*Derivative(y(x), x) + complex(0, 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]