Internal problem ID [1487]
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 23.
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 }-16 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 2, y^{\prime \prime }\relax (0) = -2, y^{\prime \prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 29
dsolve([diff(y(x),x$4)-16*y(x)=0,y(0) = 2, D(y)(0) = 2, (D@@2)(y)(0) = -2, (D@@3)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {5 \,{\mathrm e}^{2 x}}{8}+\frac {{\mathrm e}^{-2 x}}{8}+\frac {\sin \left (2 x \right )}{2}+\frac {5 \cos \left (2 x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[{y''''[x]-16*y[x]==0,{y[0]==2,y'[0]==2,y''[0]==-2,y'''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (2 \sin (2 x)+5 \cos (2 x)+2 \sinh (2 x)+3 \cosh (2 x)) \\ \end{align*}