60.3.112 problem 1116

Internal problem ID [11122]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1116
Date solved : Tuesday, January 28, 2025 at 05:41:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.099 (sec). Leaf size: 31

dsolve(x*diff(diff(y(x),x),x)+(a*x+b+n)*diff(y(x),x)+n*a*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-a x} \left (\operatorname {KummerM}\left (b , b +n , a x \right ) c_{1} +\operatorname {KummerU}\left (b , b +n , a x \right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 38

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

\[ y(x)\to e^{-a x} (c_1 \operatorname {HypergeometricU}(b,b+n,a x)+c_2 L_{-b}^{b+n-1}(a x)) \]