74.15.61 problem 64 (a)

Internal problem ID [16500]
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 : 64 (a)
Date solved : Tuesday, January 28, 2025 at 09:09:51 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(x^3*diff(y(x),x$3)+16*x^2*diff(y(x),x$2)+79*x*diff(y(x),x)+125*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[x^3*D[y[x],{x,3}]+16*x^2*D[y[x],{x,2}]+79*x*D[y[x],x]+125*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x \cos (3 \log (x))+c_1 x \sin (3 \log (x))+c_3}{x^5} \]