Internal problem ID [6945]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 214.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 33
dsolve(t*diff(y(t),t$2)+(1-t^2)*diff(y(t),t)+4*t*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (1-t^{2}+\frac {1}{8} t^{4}\right )+c_{2} \left (2-2 t^{2}+\frac {1}{4} t^{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.319 (sec). Leaf size: 55
DSolve[t*y''[t]+(1-t^2)*y'[t]+4*t*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{128} \left (\left (t^4-8 t^2+8\right ) \left (c_2 \text {Ei}\left (\frac {t^2}{2}\right )+128 c_1\right )-2 c_2 e^{\frac {t^2}{2}} \left (t^2-6\right )\right ) \\ \end{align*}