60.3.134 problem 1138

Internal problem ID [11144]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1138
Date solved : Tuesday, January 28, 2025 at 05:41:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }+4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \end{align*}

Solution by Maple

Time used: 0.099 (sec). Leaf size: 26

dsolve(4*x*diff(diff(y(x),x),x)+4*m*diff(y(x),x)-(x-2*m-4*n)*y(x)=0,y(x), singsol=all)
 
\[ y = {\mathrm e}^{-\frac {x}{2}} \left (\operatorname {KummerU}\left (-n , m , x\right ) c_{2} +\operatorname {KummerM}\left (-n , m , x\right ) c_{1} \right ) \]

Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 32

DSolve[(2*m + 4*n - x)*y[x] + 4*m*D[y[x],x] + 4*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to e^{-x/2} (c_1 \operatorname {HypergeometricU}(-n,m,x)+c_2 L_n^{m-1}(x)) \]