12.17.5 problem section 9.1, problem 5(b) 3

Internal problem ID [2111]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.1. Page 471
Problem number : section 9.1, problem 5(b) 3
Date solved : Tuesday, March 04, 2025 at 01:50:26 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ y^{\prime \prime }\left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 21

ode:=x^3*diff(diff(diff(y(x),x),x),x)-x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+6*y(x) = 0; 
ic:=y(1) = 0, D(y)(1) = 0, (D@@2)(y)(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {3 x^{4}-4 x^{3}+1}{12 x} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 24

ode=x^3*D[y[x],{x,3}]-x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+6*y[x]==0; 
ic={y[1]==0,Derivative[1][y][1]==0,Derivative[2][y][1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3 x^4-4 x^3+1}{12 x} \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 0, Subs(Derivative(y(x), (x, 2)), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{3}}{4} - \frac {x^{2}}{3} + \frac {1}{12 x} \]