Internal problem ID [6362]
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: 15.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$5)-6*diff(y(x),x$4)-8*diff(y(x),x$3)+48*diff(y(x),x$2)+16*diff(y(x),x)-96*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{6 x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-2 x} x +c_{4} {\mathrm e}^{2 x}+c_{5} {\mathrm e}^{2 x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 43
DSolve[y'''''[x]-6*y''''[x]-8*y'''[x]+48*y''[x]+16*y'[x]-96*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_2 x+c_3 e^{4 x}+c_4 e^{4 x} x+c_5 e^{8 x}+c_1\right ) \]