54.3.321 problem 1338

Internal problem ID [12616]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1338
Date solved : Wednesday, October 01, 2025 at 02:15:57 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}+\frac {y}{3 x^{2} \left (x -2\right )} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x) = 1/3/x*(6*x-1)/(x-2)*diff(y(x),x)+1/3/x^2/(x-2)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 x \left (18 x^{2}-102 x +187\right )+c_2 \,x^{{1}/{6}} \left (x -2\right )^{{17}/{6}} \]

✓ Mathematica. Time used: 0.157 (sec). Leaf size: 112

ode=D[y[x],{x,2}] == y[x]/(3*(-2 + x)*x^2) + ((-1 + 6*x)*D[y[x],x])/(3*(-2 + x)*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {1-12 K[1]}{12 K[1]-6 K[1]^2}dK[1]-\frac {1}{2} \int _1^x\frac {1-6 K[2]}{3 (K[2]-2) K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {1-12 K[1]}{12 K[1]-6 K[1]^2}dK[1]\right )dK[3]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - (6*x - 1)*Derivative(y(x), x)/(3*x*(x - 2)) - y(x)/(3*x**2*(x - 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False