71.9.12 problem 14

Internal problem ID [14420]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 14
Date solved : Monday, March 31, 2025 at 12:26:41 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 6

ode:=diff(diff(diff(y(x),x),x),x)+diff(y(x),x) = 0; 
ic:=y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \cos \left (x \right ) \]

✓ Mathematica. Time used: 60.01 (sec). Leaf size: 33

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

\[ y(x)\to \int _1^x-\sin (K[1])dK[1]-\int _1^0-\sin (K[1])dK[1]+1 \]

✓ Sympy. Time used: 0.126 (sec). Leaf size: 5

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

\[ y{\left (x \right )} = \cos {\left (x \right )} \]