68.15.30 problem 30

Internal problem ID [17756]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 30
Date solved : Thursday, October 02, 2025 at 02:27:46 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y&=\frac {1}{x^{13}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

ode:=x^3*diff(diff(diff(y(x),x),x),x)+16*x^2*diff(diff(y(x),x),x)+70*x*diff(y(x),x)+80*y(x) = 1/x^13; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {1}{648 x^{13}}+\frac {c_1}{x^{4}}+\frac {c_2}{x^{5}}+\frac {c_3 \ln \left (x \right )}{x^{4}} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 33

ode=x^3*D[y[x],{x,3}]+16*x^2*D[y[x],{x,2}]+70*x*D[y[x],x]+80*y[x]==1/x^(13); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{648 x^{13}}+\frac {c_1}{x^5}+\frac {c_2}{x^4}+\frac {c_3 \log (x)}{x^4} \end{align*}

✓ Sympy. Time used: 0.232 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 16*x**2*Derivative(y(x), (x, 2)) + 70*x*Derivative(y(x), x) + 80*y(x) - 1/x**13,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} x^{8} + 648 x^{9} \left (C_{2} + C_{3} \log {\left (x \right )}\right ) - 1}{648 x^{13}} \]