Internal problem ID [5265]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 124
Problem number: 3.
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 }+4 x y^{\prime }+\left (x^{2}+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+(2+x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \relax (x )}{x^{2}}+\frac {c_{2} \cos \relax (x )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 37
DSolve[x^2*y''[x]+4*x*y'[x]+(2+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_1 e^{-i x}-i c_2 e^{i x}}{2 x^2} \\ \end{align*}