73.13.29 problem 20.4 (e)

Internal problem ID [15407]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.4 (e)
Date solved : Tuesday, January 28, 2025 at 07:54:43 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 x y^{\prime }+16 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)+15*x^2*diff(y(x),x$2)+9*x*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+15*x^2*D[y[x],{x,2}]+9*x*D[y[x],x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 \log (x)+c_1) \cos (2 \log (x))+(c_4 \log (x)+c_3) \sin (2 \log (x)) \]