39.5.13 problem Problem 24.36

Internal problem ID [6555]
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
Date solved : Monday, January 27, 2025 at 02:12:12 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.153 (sec). Leaf size: 13

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)
 

\[ y = \frac {\cos \left (x \right )}{2}+\frac {\cosh \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 22

DSolve[{D[y[x],{x,4}]-y[x]==0,{y[0]==1,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0,Derivative[3][y][0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (e^{-x}+e^x+2 \cos (x)\right ) \]