Internal problem ID [10904]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-3 Equation of form
\((a x + b)y''+f(x)y'+g(x)y=0\)
Problem number: 70.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
\[ \boxed {x y^{\prime \prime }+\left (b -x \right ) y^{\prime }-y a=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve(x*diff(y(x),x$2)+(b-x)*diff(y(x),x)-a*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \operatorname {KummerM}\left (a , b , x\right )+c_{2} \operatorname {KummerU}\left (a , b , x\right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 24
DSolve[x*y''[x]+(b-x)*y'[x]-a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {HypergeometricU}(a,b,x)+c_2 L_{-a}^{b-1}(x) \]