Internal problem ID [1103]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page
203
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 89
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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x \left (i \sqrt {7}-1\right )}{2}} \left (3 x -1\right )^{2} \KummerM \left (\frac {3}{2}-\frac {5 i \sqrt {7}}{14}, 3, \frac {i \sqrt {7}\, \left (3 x -1\right )}{3}\right )+c_{2} {\mathrm e}^{-\frac {x \left (i \sqrt {7}-1\right )}{2}} \left (3 x -1\right )^{2} \KummerU \left (\frac {3}{2}-\frac {5 i \sqrt {7}}{14}, 3, \frac {i \sqrt {7}\, \left (3 x -1\right )}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 109
DSolve[(3*x-1)*y''[x]-(3*x+2)*y'[x]+(6*x-8)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 4 e^{\frac {1}{6} \left (1-i \sqrt {7}\right ) (3 x-1)} (1-3 x)^2 \left (c_1 \text {HypergeometricU}\left (\frac {3}{2}-\frac {5 i}{2 \sqrt {7}},3,\frac {1}{3} i \sqrt {7} (3 x-1)\right )+c_2 \text {LaguerreL}\left (-\frac {3}{2}+\frac {5 i}{2 \sqrt {7}},2,\frac {1}{3} i \sqrt {7} (3 x-1)\right )\right ) \\ \end{align*}