60.3.125 problem 1139

Internal problem ID [11121]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1139
Date solved : Sunday, March 30, 2025 at 07:43:15 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*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 37

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

\[ y = \sqrt {x}\, {\mathrm e}^{-\frac {x}{4}} \left (\operatorname {KummerU}\left (\frac {a}{8}+\frac {3}{4}, \frac {3}{2}, \frac {x}{2}\right ) c_2 +\operatorname {KummerM}\left (\frac {a}{8}+\frac {3}{4}, \frac {3}{2}, \frac {x}{2}\right ) c_1 \right ) \]

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

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(16*x*Derivative(y(x), (x, 2)) - (a + x)*y(x) + 8*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False