54.3.55 problem 1060

Internal problem ID [12350]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1060
Date solved : Friday, October 03, 2025 at 03:18:33 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+a \,x^{q -1} y^{\prime }+b \,x^{q -2} y&=0 \end{align*}

✓ Maple. Time used: 0.096 (sec). Leaf size: 71

ode:=diff(diff(y(x),x),x)+a*x^(q-1)*diff(y(x),x)+b*x^(q-2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {a \,x^{q}}{q}} x \left (\operatorname {KummerU}\left (1-\frac {b}{a q}, \frac {1}{q}+1, \frac {a \,x^{q}}{q}\right ) c_2 +\operatorname {KummerM}\left (1-\frac {b}{a q}, \frac {1}{q}+1, \frac {a \,x^{q}}{q}\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 81

ode=b*x^(-2 + q)*y[x] + a*x^(-1 + q)*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 q^{-1/q} a^{\frac {1}{q}} \left (x^q\right )^{\frac {1}{q}} \operatorname {Hypergeometric1F1}\left (\frac {a+b}{a q},1+\frac {1}{q},-\frac {a x^q}{q}\right )+c_1 \operatorname {Hypergeometric1F1}\left (\frac {b}{a q},\frac {q-1}{q},-\frac {a x^q}{q}\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
q = symbols("q") 
y = Function("y") 
ode = Eq(a*x**(q - 1)*Derivative(y(x), x) + b*x**(q - 2)*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : Add object cannot be interpreted as an integer