9.2.27 problem problem 57

Internal problem ID [961]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 57
Date solved : Tuesday, March 04, 2025 at 12:06:27 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

\[ y = c_1 +c_2 \,x^{3+\sqrt {3}}+c_3 \,x^{3-\sqrt {3}} \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 54

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

\[ y(x)\to \frac {c_2 x^{3+\sqrt {3}}}{3+\sqrt {3}}+\frac {c_1 x^{3-\sqrt {3}}}{3-\sqrt {3}}+c_3 \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 24

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)) + x*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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