74.15.65 problem 64 (e)

Internal problem ID [16504]
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 (e)
Date solved : Tuesday, January 28, 2025 at 09:09:53 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(x^4*diff(y(x),x$4)+10*x^3*diff(y(x),x$3)+27*x^2*diff(y(x),x$2)+21*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\left (c_4 \ln \left (x \right )+c_{2} \right ) \cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right ) \left (\ln \left (x \right ) c_{3} +c_{1} \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 34

DSolve[x^4*D[y[x],{x,4}]+10*x^3*D[y[x],{x,3}]+27*x^2*D[y[x],{x,2}]+21*x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(c_4 \log (x)+c_3) \cos (\log (x))+(c_2 \log (x)+c_1) \sin (\log (x))}{x} \]