Internal problem ID [1745]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
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)
\[ y \left (t \right ) = c_{2} t^{2}+c_{1} t +c_{1} +c_{2} \]
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 64
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]
\[ y(t)\to \frac {\sqrt {t^2+2 t-1} \left (c_1 \left (t^2-2 \left (\sqrt {2}-1\right ) t-2 \sqrt {2}+3\right )+c_2 (t+1)\right )}{\sqrt {-t^2-2 t+1}} \]