54.3.130 problem 1144

Internal problem ID [12425]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1144
Date solved : Friday, October 03, 2025 at 03:19:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+c y&=0 \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 145

ode:=2*a*x*diff(diff(y(x),x),x)+(b*x+3*a)*diff(y(x),x)+c*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 69

ode=c*y[x] + (3*a + b*x)*D[y[x],x] + 2*a*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(2*a*x*Derivative(y(x), (x, 2)) + c*y(x) + (3*a + b*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False