50.13.23 problem 20

Internal problem ID [8038]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 20
Date solved : Monday, January 27, 2025 at 03:37:01 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(x^3*diff(y(x),x$4)+8*x^2*diff(y(x),x$3)+8*x*diff(y(x),x$2)-8*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\frac {c_{2}}{x^{3}}+\frac {c_3}{x}+c_4 \,x^{2} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 33

DSolve[x^3*D[y[x],{x,4}]+8*x^2*D[y[x],{x,3}]+8*x*D[y[x],{x,2}]-8*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {c_1}{3 x^3}+\frac {c_3 x^2}{2}-\frac {c_2}{x}+c_4 \]