64.2.8 problem 5

Internal problem ID [13197]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:36:53 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (2\right )&=0\\ y^{\prime }\left (2\right )&=2\\ y^{\prime \prime }\left (2\right )&=6 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 18

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

\[ y(x)\to -\frac {3}{4} x \left (x^2-8 x+12\right ) \]

✓ Sympy. Time used: 0.234 (sec). Leaf size: 12

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

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