Internal problem ID [7901]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 421.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(t*diff(y(t),t$2)+ (t^2-1)*diff(y(t),t)+t^3*y(t) = 0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{-\frac {t^{2}}{4}} \cos \left (\frac {t^{2} \sqrt {3}}{4}\right )+c_{2} {\mathrm e}^{-\frac {t^{2}}{4}} \sin \left (\frac {t^{2} \sqrt {3}}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 48
DSolve[t*y''[t]+(t^2-1)*y'[t]+t^3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-\frac {t^2}{4}} \left (c_2 \cos \left (\frac {\sqrt {3} t^2}{4}\right )+c_1 \sin \left (\frac {\sqrt {3} t^2}{4}\right )\right ) \]