38.1.38 problem 40

Internal problem ID [8199]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 40
Date solved : Tuesday, September 30, 2025 at 05:18:41 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y = c_2 \,x^{4}+c_3 \,x^{2}+c_1 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {c_2 x^4}{4}+\frac {c_1 x^2}{2}+c_3 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 3)) - 3*x*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + C_{3} x^{4} \]