Internal problem ID [6340]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 49.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-3 y^{\prime } t +5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(t^2*diff(y(t),t$2)-3*t*diff(y(t),t)+5*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \sin \left (\ln \relax (t )\right ) t^{2}+c_{2} \cos \left (\ln \relax (t )\right ) t^{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 22
DSolve[t^2*y''[t]-3*t*y'[t]+5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^2 (c_2 \cos (\log (t))+c_1 \sin (\log (t))) \\ \end{align*}