60.3.135 problem 1139

Internal problem ID [11145]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1139
Date solved : Tuesday, January 28, 2025 at 05:41:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x y^{\prime \prime }+8 y^{\prime }-\left (x +a \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.197 (sec). Leaf size: 37

dsolve(16*x*diff(diff(y(x),x),x)+8*diff(y(x),x)-(x+a)*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, {\mathrm e}^{-\frac {x}{4}} \left (\operatorname {KummerM}\left (\frac {a}{8}+\frac {3}{4}, \frac {3}{2}, \frac {x}{2}\right ) c_{1} +\operatorname {KummerU}\left (\frac {a}{8}+\frac {3}{4}, \frac {3}{2}, \frac {x}{2}\right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 59

DSolve[(-a - x)*y[x] + 8*D[y[x],x] + 16*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/4} \sqrt {x} \left (c_1 \operatorname {HypergeometricU}\left (\frac {a+6}{8},\frac {3}{2},\frac {x}{2}\right )+c_2 L_{\frac {1}{8} (-a-6)}^{\frac {1}{2}}\left (\frac {x}{2}\right )\right ) \]