Internal problem ID [6749]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 12
dsolve((1-t)*diff(y(t),t$2)+t*diff(y(t),t)-y(t) = 0,y(t), singsol=all)
\[ y \relax (t ) = t c_{1}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 17
DSolve[(1-t)*y''[t]+t*y'[t]-y[t] == 0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 e^t-c_2 t \\ \end{align*}