Internal problem ID [7355]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 635.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(diff(y(t),t$2)-2*t/(1+t^2)*diff(y(t),t)+2/(1+t^2)*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = t c_{1}+c_{2} \left (t^{2}-1\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 21
DSolve[y''[t]-2*t/(1+t^2)*y'[t]+2/(1+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*}