Internal problem ID [7456]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 737.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.119 (sec). Leaf size: 25
dsolve((2*x-3)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (2 x -3\right )^{\frac {7}{4}} \KummerM \left (\frac {3}{4}, \frac {11}{4}, \frac {x}{2}-\frac {3}{4}\right )+c_{2} x \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 63
DSolve[(2*x-3)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2\operatorname {\ }2^{3/4} (2 x-3) \left (c_2 (2 x-3)^{3/4} L_{-\frac {3}{4}}^{\frac {7}{4}}\left (\frac {x}{2}-\frac {3}{4}\right )+\frac {4 \sqrt {2} c_1 x}{2 x-3}\right ) \\ \end{align*}