Internal problem ID [7701]
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]]
\[ \boxed {t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = c_{1} \left (1-t^{2}+\frac {1}{8} t^{4}\right )+c_{2} \left (2-2 t^{2}+\frac {1}{4} t^{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.42 (sec). Leaf size: 61
DSolve[t*y''[t]+(1-t^2)*y'[t]+4*t*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{128} c_2 \left (\left (t^4-8 t^2+8\right ) \operatorname {ExpIntegralEi}\left (\frac {t^2}{2}\right )-2 e^{\frac {t^2}{2}} \left (t^2-6\right )\right )+c_1 \left (t^4-8 t^2+8\right ) \]