59.1.347 problem 354

Internal problem ID [9519]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 354
Date solved : Sunday, March 30, 2025 at 02:36:41 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*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 35

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

\[ y = \frac {c_1 \left (24 t^{2}-104 t +111\right )}{24}+\frac {c_2 \left (6 t -17\right ) \left (t -2\right )^{{3}/{2}}}{\sqrt {t -3}} \]

✓ Mathematica. Time used: 0.512 (sec). Leaf size: 130

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

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

✓ Sympy. Time used: 1.046 (sec). Leaf size: 49

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((2*t - 3)*Derivative(y(t), t) + (2*t**2 - 10*t + 12)*Derivative(y(t), (t, 2)) - 8*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{2} \left (\frac {299 t^{4}}{5184} + \frac {13 t^{3}}{108} + \frac {t^{2}}{3} + 1\right ) + C_{1} t \left (\frac {851 t^{3}}{13824} + \frac {37 t^{2}}{288} + \frac {t}{8} + 1\right ) + O\left (t^{6}\right ) \]