Internal problem ID [1786]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 17
dsolve((t-1)^2*diff(y(t),t$2)-2*(t-1)*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (t -1\right )^{2}+c_{2} \left (t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 18
DSolve[(t-1)^2*y''[t]-2*(t-1)*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to (t-1) (c_2 (t-1)+c_1) \\ \end{align*}