60.3.128 problem 1132

Internal problem ID [11138]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1132
Date solved : Tuesday, January 28, 2025 at 05:41:26 PM
CAS classification : [_Laguerre]

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

✓ Solution by Maple

Time used: 0.205 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 44

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

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