23.5.4 problem 4

Internal problem ID [6613]
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 : 4
Date solved : Tuesday, September 30, 2025 at 03:50:14 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(diff(diff(y(x),x),x),x) = sin(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}}{2}+c_2 x +c_3 +\frac {7 \cos \left (x \right )}{9}-\frac {\cos \left (x \right )^{3}}{27} \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to c_3 x^2+\frac {3 \cos (x)}{4}-\frac {1}{108} \cos (3 x)+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.367 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} - \frac {\cos ^{3}{\left (x \right )}}{27} + \frac {7 \cos {\left (x \right )}}{9} \]