60.3.127 problem 1131

Internal problem ID [11137]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1131
Date solved : Tuesday, January 28, 2025 at 05:41:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+a y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.217 (sec). Leaf size: 33

dsolve(2*x*diff(diff(y(x),x),x)-(x-1)*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, \left (\operatorname {KummerU}\left (-a +\frac {1}{2}, \frac {3}{2}, \frac {x}{2}\right ) c_{2} +\operatorname {KummerM}\left (-a +\frac {1}{2}, \frac {3}{2}, \frac {x}{2}\right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 48

DSolve[a*y[x] - (-1 + x)*D[y[x],x] + 2*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} \left (c_1 \operatorname {HypergeometricU}\left (\frac {1}{2}-a,\frac {3}{2},\frac {x}{2}\right )+c_2 L_{a-\frac {1}{2}}^{\frac {1}{2}}\left (\frac {x}{2}\right )\right ) \]