Internal problem ID [5608]
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: 14.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)+diff(y(x),x$3)-3*diff(y(x),x$2)-5*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} c_{1}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{-x} x +c_{4} {\mathrm e}^{-x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[y''''[x]+y'''[x]-3*y''[x]-5*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (x (c_3 x+c_2)+c_4 e^{3 x}+c_1\right ) \\ \end{align*}