68.15.29 problem 29

Internal problem ID [17755]
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 : 29
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 }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y&=\frac {1}{x^{3}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 28

ode:=x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)-11*x*diff(y(x),x)+16*y(x) = 1/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {25 c_3 \,x^{6} \ln \left (x \right )+25 c_1 \,x^{6}+25 c_2 +x}{25 x^{4}} \]

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

ode=x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]-11*x*D[y[x],x]+16*y[x]==1/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^4}+\frac {1}{25 x^3}+c_2 x^2+c_3 x^2 \log (x) \end{align*}

✓ Sympy. Time used: 0.208 (sec). Leaf size: 22

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)) - 11*x*Derivative(y(x), x) + 16*y(x) - 1/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 25 x^{6} \left (C_{2} + C_{3} \log {\left (x \right )}\right ) + x}{25 x^{4}} \]