Internal problem ID [5228]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 79
Problem number: 2(c).
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (5)}-y^{\prime \prime \prime \prime }-y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 0, y^{\prime \prime \prime }\relax (0) = 0, y^{\prime \prime \prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 28
dsolve([diff(y(x),x$5)-diff(y(x),x$4)-diff(y(x),x)+y(x)=0,y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0, (D@@4)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-x}}{8}+\frac {\left (-2 x +5\right ) {\mathrm e}^{x}}{8}+\frac {\cos \relax (x )}{4}-\frac {\sin \relax (x )}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 32
DSolve[{y'''''[x]-y''''[x]-y'[x]+y[x]==0,{y[0]==1,y'[0]==0,y''[0]==0,y'''[0]==0,y''''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (e^x (5-2 x)+e^{-x}-2 \sin (x)+2 \cos (x)\right ) \\ \end{align*}