Internal problem ID [1738]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 31
dsolve(t^2*diff(y(t),t$2)+2*t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1} \sin \left (\frac {\sqrt {7}\, \ln \relax (t )}{2}\right )}{\sqrt {t}}+\frac {c_{2} \cos \left (\frac {\sqrt {7}\, \ln \relax (t )}{2}\right )}{\sqrt {t}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 42
DSolve[t^2*y''[t]+2*t*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {7} \log (t)\right )+c_1 \sin \left (\frac {1}{2} \sqrt {7} \log (t)\right )}{\sqrt {t}} \\ \end{align*}