60.3.130 problem 1134

Internal problem ID [11140]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1134
Date solved : Tuesday, January 28, 2025 at 05:41:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }-\left (x +a \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 21

dsolve(4*x*diff(diff(y(x),x),x)-(x+a)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {WhittakerM}\left (-\frac {a}{4}, \frac {1}{2}, x\right )+c_{2} \operatorname {WhittakerW}\left (-\frac {a}{4}, \frac {1}{2}, x\right ) \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 44

DSolve[(-a - x)*y[x] + 4*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-x/2} x \left (c_2 \operatorname {Hypergeometric1F1}\left (\frac {a}{4}+1,2,x\right )+c_1 \operatorname {HypergeometricU}\left (\frac {a}{4}+1,2,x\right )\right ) \]