Internal problem ID [1737]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+t y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(t^2*diff(y(t),t$2)+t*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \sin \left (\ln \relax (t )\right )+\cos \left (\ln \relax (t )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 18
DSolve[t^2*y''[t]+t*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 \cos (\log (t))+c_2 \sin (\log (t)) \\ \end{align*}