60.3.129 problem 1143

Internal problem ID [11125]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1143
Date solved : Sunday, March 30, 2025 at 07:43:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.041 (sec). Leaf size: 57

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

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

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 74

ode=c*y[x] + (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]
 

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

✗ 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) + (a + b*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False