7.9.7 problem 19

Internal problem ID [255]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 19
Date solved : Tuesday, March 04, 2025 at 11:06:23 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 (1\right )&=6\\ y^{\prime }\left (1\right )&=14\\ y^{\prime \prime }\left (1\right )&=22 \end{align*}

✓ Maple. Time used: 0.010 (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(1) = 6, D(y)(1) = 14, (D@@2)(y)(1) = 22; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 17

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[1]==6,Derivative[1][y][1] ==14,Derivative[2][y][1] ==22}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \left (3 x^2+2 x+1\right ) \]

✓ Sympy. Time used: 0.243 (sec). Leaf size: 14

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(1): 6, Subs(Derivative(y(x), x), x, 1): 14, Subs(Derivative(y(x), (x, 2)), x, 1): 22} 
dsolve(ode,func=y(x),ics=ics)
 

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