Internal problem ID [679]
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: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 13
dsolve(2*t^2*diff(y(t),t$2)-5*t*diff(y(t),t)+5*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t +c_{2} t^{\frac {5}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[2*t^2*y''[t]-5*t*y'[t]+5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t \left (c_2 t^{3/2}+c_1\right ) \\ \end{align*}