Internal problem ID [1789]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((t-2)^2*diff(y(t),t$2)+5*(t-2)*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1}}{\left (t -2\right )^{2}}+\frac {c_{2} \ln \left (t -2\right )}{\left (t -2\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 22
DSolve[(t-2)^2*y''[t]+5*(t-2)*y'[t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2 c_2 \log (t-2)+c_1}{(t-2)^2} \\ \end{align*}