14.13.3 problem 3

Internal problem ID [2630]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.8.1, singular points, Euler equations. Excercises page 203
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:04:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve((t-1)^2*diff(y(t),t$2)-2*(t-1)*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
 

\[ y = \left (-1+t \right ) \left (\left (-1+t \right ) c_1 +c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 18

DSolve[(t-1)^2*D[y[t],{t,2}]-2*(t-1)*D[y[t],t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to (t-1) (c_2 (t-1)+c_1) \]