59.1.290 problem 293

Internal problem ID [9462]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 293
Date solved : Monday, January 27, 2025 at 06:03:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 29

dsolve((2*x-3)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = 2 \left (2 x -3\right )^{{3}/{4}} \left (x -\frac {3}{2}\right ) c_{1} \operatorname {KummerM}\left (\frac {3}{4}, \frac {11}{4}, \frac {x}{2}-\frac {3}{4}\right )+c_{2} x \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 63

DSolve[(2*x-3)*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2\ 2^{3/4} (2 x-3) \left (c_2 (2 x-3)^{3/4} L_{-\frac {3}{4}}^{\frac {7}{4}}\left (\frac {x}{2}-\frac {3}{4}\right )+\frac {4 \sqrt {2} c_1 x}{2 x-3}\right ) \]