Internal problem ID [5066]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number: 58.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (\frac {\sqrt {15}\, \ln \relax (x )}{2}\right )}{\sqrt {x}}+\frac {c_{2} \cos \left (\frac {\sqrt {15}\, \ln \relax (x )}{2}\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 42
DSolve[x^2*y''[x]+2*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {15} \log (x)\right )+c_1 \sin \left (\frac {1}{2} \sqrt {15} \log (x)\right )}{\sqrt {x}} \\ \end{align*}