Internal problem ID [9468]
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]]
\[ \boxed {4 y^{\prime \prime } x +4 m y^{\prime }-\left (x -2 m -4 n \right ) y=0} \]
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \left (\operatorname {KummerM}\left (-n , m , x\right ) c_{1} +\operatorname {KummerU}\left (-n , m , x\right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.04 (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]
\[ y(x)\to e^{-x/2} (c_1 \operatorname {HypergeometricU}(-n,m,x)+c_2 L_n^{m-1}(x)) \]