Internal problem ID [5285]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 16
dsolve(x^2*diff(y(x),x$2)-(2+I)*x*diff(y(x),x)+3*I*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{i}+c_{2} x^{3} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 20
DSolve[x^2*y''[x]-(2+I)*x*y'[x]+3*I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^i+c_2 x^3 \\ \end{align*}