87.13.36 problem 40

Internal problem ID [23519]
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 100
Problem number : 40
Date solved : Thursday, October 02, 2025 at 09:42:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 y^{\prime \prime }+\frac {3 y^{\prime }}{x -3}+\frac {3 y}{\left (x -3\right )^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 35

ode:=5*diff(diff(y(x),x),x)+3/(x-3)*diff(y(x),x)+3/(x-3)^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x -3\right )^{{1}/{5}} \left (c_1 \sin \left (\frac {\sqrt {14}\, \ln \left (x -3\right )}{5}\right )+c_2 \cos \left (\frac {\sqrt {14}\, \ln \left (x -3\right )}{5}\right )\right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 48

ode=5*D[y[x],{x,2}]+3/(x-3)*D[y[x],x]+3/(x-3)^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt [5]{x-3} \left (c_2 \cos \left (\frac {1}{5} \sqrt {14} \log (x-3)\right )+c_1 \sin \left (\frac {1}{5} \sqrt {14} \log (x-3)\right )\right ) \end{align*}

✓ Sympy. Time used: 0.174 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), x)/(x - 3) + 3*y(x)/(x - 3)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt [5]{x - 3} \]