Internal problem ID [7516]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 799.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 t \left (t +1\right ) y^{\prime \prime }+y^{\prime } t -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.127 (sec). Leaf size: 68
dsolve(3*t*(1+t)*diff(y(t),t$2)+t*diff(y(t),t)-y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = t c_{1}+c_{2} \left (2 \sqrt {3}\, \arctan \left (\frac {2 \sqrt {3}\, \left (t +1\right )^{\frac {1}{3}}}{3}+\frac {\sqrt {3}}{3}\right ) t +6 \left (t +1\right )^{\frac {2}{3}}+2 \ln \left (\left (t +1\right )^{\frac {1}{3}}-1\right ) t -\ln \left (\left (t +1\right )^{\frac {2}{3}}+\left (t +1\right )^{\frac {1}{3}}+1\right ) t \right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 90
DSolve[3*t*(1+t)*y''[t]+t*y'[t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 t \left (-2 \sqrt {3} \operatorname {ArcTan}\left (\frac {2 \sqrt [3]{t+1}+1}{\sqrt {3}}\right )-2 \log \left (\sqrt [3]{t+1}-1\right )+\log \left ((t+1)^{2/3}+\sqrt [3]{t+1}+1\right )\right )+6 c_1 t-6 c_2 (t+1)^{2/3}}{6 \sqrt [6]{3}} \\ \end{align*}