64.13.22 problem 22

Internal problem ID [13481]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 22
Date solved : Monday, March 31, 2025 at 07:59:12 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=-5 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 15

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

\[ y = \frac {-x^{2}+2}{x^{3}} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 16

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

\[ y(x)\to \frac {2-x^2}{x^3} \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 10

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

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