Internal problem ID [4343]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 16 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x y^{\prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \sin \left (\sqrt {5}\, \ln \relax (x )\right )+c_{2} x \cos \left (\sqrt {5}\, \ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 32
DSolve[x^2*y''[x]-x*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (c_2 \cos \left (\sqrt {5} \log (x)\right )+c_1 \sin \left (\sqrt {5} \log (x)\right )\right ) \\ \end{align*}