Internal problem ID [1748]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 15
dsolve((1+t^2)*diff(y(t),t$2)-2*t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t +c_{2} \left (t^{2}-1\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 21
DSolve[(1+t^2)*y''[t]-2*t*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_2 t-c_1 (t-i)^2 \\ \end{align*}