74.15.16 problem 16

Internal problem ID [16455]
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 : 16
Date solved : Tuesday, January 28, 2025 at 09:08:21 AM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(x^3*diff(y(x),x$3)+4*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 28

DSolve[x^3*D[y[x],{x,3}]+4*x^2*D[y[x],{x,2}]+6*x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_3}{x}+c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x)) \]