Internal problem ID [1488]
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 24.
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 }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -2, y^{\prime }\relax (0) = -8, y^{\prime \prime }\relax (0) = -14, y^{\prime \prime \prime }\relax (0) = -62] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve([diff(y(x),x$4)-6*diff(y(x),x$3)+7*diff(y(x),x$2)+6*diff(y(x),x)-8*y(x)=0,y(0) = -2, D(y)(0) = -8, (D@@2)(y)(0) = -14, (D@@3)(y)(0) = -62],y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{4 x}+{\mathrm e}^{2 x}+2 \,{\mathrm e}^{-x}-4 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[{y''''[x]-6*y'''[x]+7*y''[x]+6*y'[x]-8*y[x]==0,{y[0]==-2,y'[0]==-8,y''[0]==-14,y'''[0]==-62}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^{-x}-4 e^x+e^{2 x}-e^{4 x} \\ \end{align*}