38.1.57 problem 72

Internal problem ID [8218]
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 : 72
Date solved : Tuesday, September 30, 2025 at 05:19:00 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)+20*x*diff(y(x),x)-78*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{4}+c_2 \sin \left (5 \ln \left (x \right )\right )+c_3 \cos \left (5 \ln \left (x \right )\right )}{x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 32

ode=x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]+20*x*D[y[x],x]-78*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_3 x^4+c_2 \cos (5 \log (x))+c_1 \sin (5 \log (x))}{x} \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 2*x**2*Derivative(y(x), (x, 2)) + 20*x*Derivative(y(x), x) - 78*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{3} + \frac {C_{2} \sin {\left (5 \log {\left (x \right )} \right )} + C_{3} \cos {\left (5 \log {\left (x \right )} \right )}}{x} \]