49.16.7 problem 2(b)

Internal problem ID [7705]
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)
Date solved : Monday, January 27, 2025 at 03:10:11 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = x^{2} \left (c_{1} \sin \left (\ln \left (x \right )\right )+c_{2} \cos \left (\ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (c_2 \cos (\log (x))+c_1 \sin (\log (x))) \]