Internal problem ID [5617]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (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)
\[ y \relax (x ) = c_{1}+c_{2} x^{2}+\frac {c_{3}}{x^{3}}+\frac {c_{4}}{x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 33
DSolve[x^3*y''''[x]+8*x^2*y'''[x]+8*x*y''[x]-8*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {c_1}{3 x^3}+\frac {c_3 x^2}{2}-\frac {c_2}{x}+c_4 \\ \end{align*}