Internal problem ID [8112]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 636.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4 t +4\right ) y=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 78
dsolve(diff(y(t),t$2)+(t^2+2*t+1)*diff(y(t),t)-(4+4*t)*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} \left (t^{4}+4 t^{3}+6 t^{2}+8 t +5\right )+c_{2} \left (t +1\right ) \left (t^{3}+3 t^{2}+3 t +5\right ) \left (\int \frac {{\mathrm e}^{-\frac {t \left (t^{2}+3 t +3\right )}{3}}}{\left (t +1\right )^{2} \left (t^{3}+3 t^{2}+3 t +5\right )^{2}}d t \right ) \]
✓ Solution by Mathematica
Time used: 0.369 (sec). Leaf size: 132
DSolve[y''[t]+(t^2+2*t+1)*y'[t]-(4+4*t)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{36} e^{-\frac {1}{3} t \left (t^2+3 t+3\right )} \left (-3 c_2 \left (t^3+3 t^2+3 t+4\right )+3^{2/3} c_2 e^{\frac {1}{3} (t+1)^3} \sqrt [3]{(t+1)^3} \left (t^3+3 t^2+3 t+5\right ) \Gamma \left (\frac {2}{3},\frac {1}{3} (t+1)^3\right )+36 c_1 e^{\frac {t^3}{3}+t^2+t} \left (t^4+4 t^3+6 t^2+8 t+5\right )\right ) \]