13.9.10 problem 13

Internal problem ID [2396]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 13
Date solved : Monday, January 27, 2025 at 05:51:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y = c_2 \,t^{2}+c_1 t -c_2 \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 21

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

\[ y(t)\to c_2 t-c_1 (t-i)^2 \]