Internal problem ID [6926]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 194.
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 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(diff(y(t),t$2)-2*(t+1)/(t^2+2*t-1)*diff(y(t),t)+2/(t^2+2*t-1)*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (t +1\right )+c_{2} \left (t^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 60
DSolve[y''[t]-2*(t+1)/(t^2+2*t-1)*y'[t]+2/(t^2+2*t-1)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\sqrt {t (t+2)-1} \left (c_1 \left (t \left (t-2 \sqrt {2}+2\right )-2 \sqrt {2}+3\right )+c_2 (t+1)\right )}{\sqrt {1-t (t+2)}} \\ \end{align*}