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 : Monday, January 27, 2025 at 03:10:14 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*}

✓ Solution by Maple

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

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

\[ y = c_{1} x^{3}+c_{2} x^{i} \]

✓ Solution by Mathematica

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

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

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