Internal problem ID [681]
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: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 17
dsolve(4*t^2*diff(y(t),t$2)-8*t*diff(y(t),t)+9*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t^{\frac {3}{2}}+c_{2} t^{\frac {3}{2}} \ln \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 25
DSolve[4*t^2*y''[t]-8*t*y'[t]+9*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} t^{3/2} (3 c_2 \log (t)+2 c_1) \\ \end{align*}