Internal problem ID [7023]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 293.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = c_{1} \left (-3+2 x \right )^{\frac {7}{4}} \operatorname {KummerM}\left (\frac {3}{4}, \frac {11}{4}, -\frac {3}{4}+\frac {x}{2}\right )+c_{2} x \]
✓ 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\ 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*}