67.10.13 problem 15.5 (c)

Internal problem ID [16595]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.5 (c)
Date solved : Thursday, October 02, 2025 at 01:36:48 PM
CAS classification : [[_high_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=4 \\ y^{\prime \prime }\left (0\right )&=0 \\ y^{\prime \prime \prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 13

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = 0; 
ic:=[y(0) = 0, D(y)(0) = 4, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \sin \left (x \right )+2 \sinh \left (x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to -e^{-x}+e^x+2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 15

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

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