60.3.88 problem 1092

Internal problem ID [11098]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1092
Date solved : Tuesday, January 28, 2025 at 05:41:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 53

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

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