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 : Sunday, March 30, 2025 at 11:07:16 AM
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*}

✓ Maple. Time used: 0.118 (sec). Leaf size: 13

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0; 
dsolve([ode,ic],y(x),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), (x, 4)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 0, Subs(Derivative(y(x), (x, 3)), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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