Internal problem ID [8114]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 639.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve(2*t*diff(y(t),t$2)+(1+t)*diff(y(t),t)-2*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} \left (t^{2}+6 t +3\right )+c_{2} \left (t^{2}+6 t +3\right ) \left (\int \frac {{\mathrm e}^{-\frac {t}{2}}}{\left (t^{2}+6 t +3\right )^{2} \sqrt {t}}d t \right ) \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 71
DSolve[2*t*y''[t]+(1+t)*y'[t]-2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{24} \left (\sqrt {2 \pi } c_2 \left (t^2+6 t+3\right ) \text {erf}\left (\frac {\sqrt {t}}{\sqrt {2}}\right )+24 c_1 \left (t^2+6 t+3\right )+2 c_2 e^{-t/2} \sqrt {t} (t+5)\right ) \]