Internal problem ID [8713]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1133.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 47
dsolve((2*x-1)*diff(diff(y(x),x),x)-(3*x-4)*diff(y(x),x)+(x-3)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{\frac {x}{2}} \KummerM \left (1, \frac {3}{4}, \frac {x}{2}-\frac {1}{4}\right )}{\left (2 x -1\right )^{\frac {1}{4}}}+\frac {c_{2} {\mathrm e}^{\frac {x}{2}} \KummerU \left (1, \frac {3}{4}, \frac {x}{2}-\frac {1}{4}\right )}{\left (2 x -1\right )^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 47
DSolve[(-3 + x)*y[x] - (-4 + 3*x)*y'[x] + (-1 + 2*x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{x-\frac {1}{2}} \left (\sqrt [4]{2} c_2 \text {Gamma}\left (-\frac {1}{4},\frac {1}{4} (2 x-1)\right )-8 c_1\right )}{4\ 2^{3/8}} \\ \end{align*}