Internal problem ID [9469]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1134.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 y^{\prime \prime } x -y \left (x +a \right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve(4*x*diff(diff(y(x),x),x)-(x+a)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {WhittakerM}\left (-\frac {a}{4}, \frac {1}{2}, x\right )+c_{2} \operatorname {WhittakerW}\left (-\frac {a}{4}, \frac {1}{2}, x\right ) \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 44
DSolve[(-a - x)*y[x] + 4*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-x/2} x \left (c_2 \operatorname {Hypergeometric1F1}\left (\frac {a}{4}+1,2,x\right )+c_1 \operatorname {HypergeometricU}\left (\frac {a}{4}+1,2,x\right )\right ) \]