74.15.21 problem 21

Internal problem ID [16381]
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 : 21
Date solved : Thursday, March 13, 2025 at 08:11:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\frac {1}{x^{5}} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = 1/x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{2}}{x^{2}}+\frac {\ln \left (x \right ) c_{1}}{x^{2}}+\frac {1}{9 x^{5}} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 28

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==1/x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{9 x^5}+\frac {c_1}{x^2}+\frac {2 c_2 \log (x)}{x^2} \]

✓ Sympy. Time used: 0.268 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 4*y(x) - 1/x**5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {9 x^{3} \left (C_{1} + C_{2} \log {\left (x \right )}\right ) + 1}{9 x^{5}} \]