Internal problem ID [1458]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.1. Page 471
Problem number: section 9.1, problem 3.
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 }-7 y^{\prime \prime }-y^{\prime }+6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 5, y^{\prime }\relax (0) = -6, y^{\prime \prime }\relax (0) = 10, y^{\prime \prime \prime }\relax (0) = -36] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve([diff(y(x),x$4)+diff(y(x),x$3)-7*diff(y(x),x$2)-diff(y(x),x)+6*y(x)=0,y(0) = 5, D(y)(0) = -6, (D@@2)(y)(0) = 10, (D@@3)(y)(0) = -36],y(x), singsol=all)
\[ y \relax (x ) = \left (-{\mathrm e}^{5 x}+2 \,{\mathrm e}^{4 x}+3 \,{\mathrm e}^{2 x}+1\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[{y''''[x]+y'''[x]-7*y''[x]-y'[x]+6*y[x]==0,{y[0]==5,y'[0]==-6,y''[0]==10,y'''[0]==-36}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x}+3 e^{-x}+2 e^x-e^{2 x} \\ \end{align*}