59.1.346 problem 353

Internal problem ID [9518]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 353
Date solved : Monday, January 27, 2025 at 06:03:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 56

dsolve(4*(t^2-3*t+2)*diff(y(t),t$2)-2*diff(y(t),t)+y(t)=0,y(t), singsol=all)
 

\[ y = c_{1} \sqrt {t -1}+\frac {c_{2} \left (-\frac {\sqrt {t^{2}-3 t +2}\, \left (-\ln \left (2\right )+\ln \left (-3+2 t +2 \sqrt {\left (t -1\right ) \left (t -2\right )}\right )\right )}{2}+t -2\right )}{\sqrt {t -2}} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 112

DSolve[4*(t^2-3*t+2)*D[y[t],{t,2}]-2*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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