87.13.29 problem 33

Internal problem ID [23512]
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 : 33
Date solved : Thursday, October 02, 2025 at 09:42:35 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = c_2 \,x^{5}+c_1 x \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to x \left (c_2 x^4+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} x^{4}\right ) \]