Internal problem ID [8718]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1138.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime } x +4 y^{\prime } m -\left (x -2 m -4 n \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x}{2}} \KummerM \left (-n , m , x\right )+c_{2} {\mathrm e}^{-\frac {x}{2}} \KummerU \left (-n , m , x\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 32
DSolve[(2*m + 4*n - x)*y[x] + 4*m*y'[x] + 4*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/2} (c_1 \text {HypergeometricU}(-n,m,x)+c_2 L_n^{m-1}(x)) \\ \end{align*}