Internal problem ID [5284]
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(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\ln \relax (x )\right ) x^{2}+c_{2} \cos \left (\ln \relax (x )\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 22
DSolve[x^2*y''[x]-3*x*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (c_2 \cos (\log (x))+c_1 \sin (\log (x))) \\ \end{align*}