7.9.8 problem 20

Internal problem ID [256]
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 : 20
Date solved : Saturday, March 29, 2025 at 04:49:21 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=5\\ y^{\prime \prime }\left (1\right )&=-11 \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 17

ode:=x^3*diff(diff(diff(y(x),x),x),x)+6*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-4*y(x) = 0; 
ic:=y(1) = 1, D(y)(1) = 5, (D@@2)(y)(1) = -11; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

ode=x^3*D[y[x],{x,3}]+6*x^2*D[y[x],{x,2}]+4*x*D[y[x],x]-4*y[x]==0; 
ic={y[1]==1,Derivative[1][y][1] ==5,Derivative[2][y][1] ==-11}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 x^3+\log (x)-1}{x^2} \]

✓ Sympy. Time used: 0.270 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 6*x**2*Derivative(y(x), (x, 2)) + 4*x*Derivative(y(x), x) - 4*y(x),0) 
ics = {y(1): 1, Subs(Derivative(y(x), x), x, 1): 5, Subs(Derivative(y(x), (x, 2)), x, 1): -11} 
dsolve(ode,func=y(x),ics=ics)
 

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