59.1.776 problem 798

Internal problem ID [9948]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 798
Date solved : Monday, January 27, 2025 at 06:16:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 35

dsolve(2*(t^2-5*t+6)*diff(y(t),t$2)+(2*t-3)*diff(y(t),t)-8*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {c_{1} \left (24 t^{2}-104 t +111\right )}{24}+\frac {c_{2} \left (6 t -17\right ) \left (t -2\right )^{{3}/{2}}}{\sqrt {t -3}} \]

✓ Solution by Mathematica

Time used: 0.524 (sec). Leaf size: 130

DSolve[2*(t^2-5*t+6)*D[y[t],{t,2}]+(2*t-3)*D[y[t],t]-8*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{6} (6 t-17) \exp \left (\int _1^t\frac {1}{4} \left (\frac {5}{K[1]-2}+\frac {1}{K[1]-3}\right )dK[1]-\frac {1}{2} \int _1^t\frac {2 K[2]-3}{2 \left (K[2]^2-5 K[2]+6\right )}dK[2]\right ) \left (c_2 \int _1^t\frac {36 \exp \left (-2 \int _1^{K[3]}\frac {1}{4} \left (\frac {5}{K[1]-2}+\frac {1}{K[1]-3}\right )dK[1]\right )}{(17-6 K[3])^2}dK[3]+c_1\right ) \]