Internal problem ID [5283]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+4 y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = \sin \left (2 \ln \relax (x )\right ) c_{2}+\cos \left (2 \ln \relax (x )\right ) c_{1}+\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 25
DSolve[x^2*y''[x]+x*y'[x]+4*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x))+\frac {1}{4} \\ \end{align*}