64.1.12 problem 5(b)

Internal problem ID [13178]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 5(b)
Date solved : Wednesday, March 05, 2025 at 09:19:53 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)-10*x*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{3} x^{6}+c_{1} x +c_{2}}{x^{2}} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 22

ode=x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-10*x*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_3 x^6+c_2 x+c_1}{x^2} \]

✓ Sympy. Time used: 0.225 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 2*x**2*Derivative(y(x), (x, 2)) - 10*x*Derivative(y(x), x) - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} + \frac {C_{2}}{x} + C_{3} x^{4} \]