60.3.101 problem 1115

Internal problem ID [11097]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1115
Date solved : Sunday, March 30, 2025 at 07:42:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 47

ode:=x*diff(diff(y(x),x),x)-(3*x-2)*diff(y(x),x)-(2*x-3)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x \left (-3+\sqrt {17}\right )}{2}} \left (\operatorname {KummerU}\left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) c_2 +\operatorname {KummerM}\left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 63

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

\[ y(x)\to e^{-\frac {1}{2} \left (\sqrt {17}-3\right ) x} \left (c_2 \operatorname {Hypergeometric1F1}\left (1-\frac {6}{\sqrt {17}},2,\sqrt {17} x\right )+c_1 \operatorname {HypergeometricU}\left (1-\frac {6}{\sqrt {17}},2,\sqrt {17} x\right )\right ) \]

✗ Sympy

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

False