73.13.30 problem 20.4 (f)

Internal problem ID [15408]
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 (f)
Date solved : Tuesday, January 28, 2025 at 07:54:43 AM
CAS classification : [[_high_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

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

\[ y = \frac {c_{2} x^{6}+c_4 \,x^{4}+x^{2} c_{3} +c_{1}}{x^{3}} \]

✓ 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}]-3*x^2*D[y[x],{x,2}]-9*x*D[y[x],x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_4 x^3+\frac {c_1}{x^3}+c_3 x+\frac {c_2}{x} \]