59.1.44 problem 46

Internal problem ID [9216]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 46
Date solved : Monday, January 27, 2025 at 05:52:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve((3*x-1)*diff(y(x),x$2)-(3*x+2)*diff(y(x),x)-(6*x-8)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} x \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.243 (sec). Leaf size: 94

DSolve[(3*x-1)*D[y[x],{x,2}]-(3*x+2)*D[y[x],x]-(6*x-8)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {6-9 K[1]}{2-6 K[1]}dK[1]-\frac {1}{2} \int _1^x\left (\frac {3}{1-3 K[2]}-1\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {6-9 K[1]}{2-6 K[1]}dK[1]\right )dK[3]+c_1\right ) \]