20.6.15 problem Problem 37

Internal problem ID [3710]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 37
Date solved : Tuesday, March 04, 2025 at 05:08:06 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = c_{1} +c_{2} x^{\sqrt {7}}+c_3 \,x^{-\sqrt {7}} \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 41

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

\[ y(x)\to -\frac {c_1 x^{-\sqrt {7}}}{\sqrt {7}}+\frac {c_2 x^{\sqrt {7}}}{\sqrt {7}}+c_3 \]

✓ Sympy. Time used: 0.185 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} + \frac {C_{2}}{x^{\sqrt {7}}} + C_{3} x^{\sqrt {7}} \]