73.13.32 problem 20.4 (h)

Internal problem ID [15410]
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 (h)
Date solved : Tuesday, January 28, 2025 at 07:54:44 AM
CAS classification : [[_high_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)+7*x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+7*x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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