23.5.3 problem 3

Internal problem ID [6612]
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 : 3
Date solved : Tuesday, September 30, 2025 at 03:50:14 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = \frac {c_1 \,x^{2}}{2}-\cos \left (x \right )+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.030 (sec). Leaf size: 15

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

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