23.5.10 problem 10

Internal problem ID [6619]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 03:50:17 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(y(x),x)+diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \sin \left (x \right )+c_3 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to -c_2 \cos (x)+c_1 \sin (x)+c_3 \end{align*}

✓ Sympy. Time used: 0.057 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (x \right )} + C_{3} \cos {\left (x \right )} \]