60.3.92 problem 1096

Internal problem ID [11102]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1096
Date solved : Tuesday, January 28, 2025 at 05:41:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.177 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 55

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

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