65.12.9 problem 19.1 (ix)

Internal problem ID [13725]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 19, CauchyEuler equations. Exercises page 174
Problem number : 19.1 (ix)
Date solved : Wednesday, March 05, 2025 at 10:14:04 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z&=0 \end{align*}

With initial conditions

\begin{align*} z \left (1\right )&=2\\ z^{\prime }\left (1\right )&=-1 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 16

ode:=3*x^2*diff(diff(z(x),x),x)+5*x*diff(z(x),x)-z(x) = 0; 
ic:=z(1) = 2, D(z)(1) = -1; 
dsolve([ode,ic],z(x), singsol=all);
 

\[ z = \frac {3 x^{{4}/{3}}+5}{4 x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 21

ode=3*x^2*D[z[x],{x,2}]+5*x*D[z[x],x]-z[x]==0; 
ic={z[1]==2,Derivative[1][z][1]==-1}; 
DSolve[{ode,ic},z[x],x,IncludeSingularSolutions->True]
 

\[ z(x)\to \frac {3 x^{4/3}+5}{4 x} \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
z = Function("z") 
ode = Eq(3*x**2*Derivative(z(x), (x, 2)) + 5*x*Derivative(z(x), x) - z(x),0) 
ics = {z(1): 2, Subs(Derivative(z(x), x), x, 1): -1} 
dsolve(ode,func=z(x),ics=ics)
 

\[ z{\left (x \right )} = \frac {3 \sqrt [3]{x}}{4} + \frac {5}{4 x} \]