Internal problem ID [8695]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1115.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 55
dsolve(x*diff(diff(y(x),x),x)-(3*x-2)*diff(y(x),x)-(2*x-3)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \KummerM \left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) {\mathrm e}^{-\frac {x \left (-3+\sqrt {17}\right )}{2}}+c_{2} \KummerU \left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) {\mathrm e}^{-\frac {x \left (-3+\sqrt {17}\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 63
DSolve[(3 - 2*x)*y[x] - (-2 + 3*x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {1}{2} \left (\sqrt {17}-3\right ) x} \left (c_1 \text {HypergeometricU}\left (1-\frac {6}{\sqrt {17}},2,\sqrt {17} x\right )+c_2 \, _1F_1\left (1-\frac {6}{\sqrt {17}};2;\sqrt {17} x\right )\right ) \\ \end{align*}