60.3.314 problem 1331

Internal problem ID [11310]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1331
Date solved : Sunday, March 30, 2025 at 08:13:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x) = 1/2/x*(-4+x)/(x-2)*diff(y(x),x)-1/2*(x-3)/x^2/(x-2)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sqrt {x}+c_2 \sqrt {x \left (x -2\right )} \]

✓ Mathematica. Time used: 0.297 (sec). Leaf size: 57

ode=D[y[x],{x,2}] == -1/2*((-3 + x)*y[x])/((-2 + x)*x^2) + ((-4 + x)*D[y[x],x])/(2*(-2 + x)*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt [4]{x-2} \left (2 c_2 \sqrt {x-2}+c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {1}{2 (K[1]-2)}-\frac {1}{K[1]}\right )dK[1]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - (x - 4)*Derivative(y(x), x)/(2*x*(x - 2)) + (x - 3)*y(x)/(2*x**2*(x - 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False