23.3.240 problem 242

Internal problem ID [5954]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 242
Date solved : Friday, October 03, 2025 at 01:45:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.043 (sec). Leaf size: 69

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

\[ y = {\mathrm e}^{-\frac {i \sqrt {b}\, x}{4}} \sqrt {x}\, \left (\operatorname {KummerM}\left (\frac {i a +6 \sqrt {b}}{8 \sqrt {b}}, \frac {3}{2}, \frac {i \sqrt {b}\, x}{2}\right ) c_1 +\operatorname {KummerU}\left (\frac {i a +6 \sqrt {b}}{8 \sqrt {b}}, \frac {3}{2}, \frac {i \sqrt {b}\, x}{2}\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 96

ode=(a + b*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]
 

\begin{align*} y(x)&\to \sqrt {x} e^{-\frac {1}{4} i \sqrt {b} x} \left (c_1 \operatorname {HypergeometricU}\left (\frac {i a}{8 \sqrt {b}}+\frac {3}{4},\frac {3}{2},\frac {1}{2} i \sqrt {b} x\right )+c_2 L_{-\frac {i a}{8 \sqrt {b}}-\frac {3}{4}}^{\frac {1}{2}}\left (\frac {1}{2} i \sqrt {b} x\right )\right ) \end{align*}

✗ Sympy

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

False