54.3.307 problem 1324

Internal problem ID [12602]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1324
Date solved : Wednesday, October 01, 2025 at 02:12:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x) = 1/x*(5*x-4)/(x-1)*diff(y(x),x)-(9*x-6)/x^2/(x-1)*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 98

ode=D[y[x],{x,2}] == -(((-6 + 9*x)*y[x])/((-1 + x)*x^2)) + ((-4 + 5*x)*D[y[x],x])/((-1 + x)*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\left (\frac {1}{K[1]}+\frac {1}{2-2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^x\left (\frac {1}{1-K[2]}-\frac {4}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]-2}{2 (K[1]-1) K[1]}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)) - (5*x - 4)*Derivative(y(x), x)/(x*(x - 1)) + (9*x - 6)*y(x)/(x**2*(x - 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False