Internal problem ID [7093]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 365.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {u^{\prime \prime }+\frac {u}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(u(x),x$2)+1/x^2*u(x)=0,u(x), singsol=all)
\[ u \left (x \right ) = c_{1} \sqrt {x}\, \sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right )+c_{2} \sqrt {x}\, \cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 42
DSolve[u''[x]+1/x^2*u[x]==0,u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \sqrt {x} \left (c_1 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )\right ) \\ \end{align*}