Internal problem ID [682]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 45.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 25
dsolve(t^2*diff(y(t),t$2)+5*t*diff(y(t),t)+13*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1} \sin \left (3 \ln \relax (t )\right )}{t^{2}}+\frac {c_{2} \cos \left (3 \ln \relax (t )\right )}{t^{2}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 26
DSolve[t^2*y''[t]+5*t*y'[t]+13*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 \cos (3 \log (t))+c_1 \sin (3 \log (t))}{t^2} \\ \end{align*}