Internal problem ID [1490]
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 26.
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 }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 5, y^{\prime }\relax (0) = -2, y^{\prime \prime }\relax (0) = 6, y^{\prime \prime \prime }\relax (0) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 28
dsolve([diff(y(x),x$4)+2*diff(y(x),x$3)-2*diff(y(x),x$2)-8*diff(y(x),x)-8*y(x)=0,y(0) = 5, D(y)(0) = -2, (D@@2)(y)(0) = 6, (D@@3)(y)(0) = 8],y(x), singsol=all)
\[ y \relax (x ) = \left ({\mathrm e}^{4 x}+1+\left (3 \cos \relax (x )+\sin \relax (x )\right ) {\mathrm e}^{x}\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 29
DSolve[{y''''[x]+2*y'''[x]-2*y''[x]-8*y'[x]-8*y[x]==0,{y[0]==5,y'[0]==-2,y''[0]==6,y'''[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^{4 x}+e^x (\sin (x)+3 \cos (x))+1\right ) \\ \end{align*}