Internal problem ID [680]
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: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+3 t y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1}}{t}+\frac {c_{2} \ln \relax (t )}{t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 17
DSolve[t^2*y''[t]+3*t*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 \log (t)+c_1}{t} \\ \end{align*}