87.10.15 problem 16

Internal problem ID [23416]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 79
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:41:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1}&=0 \end{align*}

✗ Maple

ode:=(x^2-4)*diff(diff(y(x),x),x)+3*x^3*diff(y(x),x)+4/(x-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^2-4)*D[y[x],{x,2}]+3*x^3*D[y[x],x]+4/(x-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**3*Derivative(y(x), x) + (x**2 - 4)*Derivative(y(x), (x, 2)) + 4*y(x)/(x - 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False