9.2.26 problem problem 56

Internal problem ID [960]
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 56
Date solved : Tuesday, March 04, 2025 at 12:06:26 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: 0.003 (sec). Leaf size: 16

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);
 

\[ y = c_3 \ln \left (x \right )^{2}+c_2 \ln \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 23

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]
 

\[ y(x)\to \frac {1}{2} c_2 \log ^2(x)+c_1 \log (x)+c_3 \]

✓ Sympy. Time used: 0.155 (sec). Leaf size: 15

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)
 

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