Internal problem ID [4704]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page
248
Problem number: Problem 24.36.
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=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] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([diff(y(x),x$4)-y(x)=0,y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-x}}{4}+\frac {{\mathrm e}^{x}}{4}+\frac {\cos \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 14
DSolve[{y''''[x]-y[x]==0,{y[0]==1,y'[0]==0,y''[0]==0,y'''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (\cos (x)+\cosh (x)) \\ \end{align*}