49.16.6 problem 2(a)

Internal problem ID [7704]
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(a)
Date solved : Monday, January 27, 2025 at 03:10:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=1,y(x), singsol=all)
 

\[ y = \sin \left (2 \ln \left (x \right )\right ) c_{2} +\cos \left (2 \ln \left (x \right )\right ) c_{1} +\frac {1}{4} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+4*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x))+\frac {1}{4} \]