Internal problem ID [1478]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient.
Page 483
Problem number: section 9.2, problem 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 }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 26
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+7*diff(y(x),x$2)-6*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} x \,{\mathrm e}^{x}+c_{3} \sin \relax (x ) {\mathrm e}^{x}+c_{4} \cos \relax (x ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[y''''[x]-4*y'''[x]+7*y''[x]-6*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_4 x+c_2 \cos (x)+c_1 \sin (x)+c_3) \\ \end{align*}