23.5.125 problem 125

Internal problem ID [6734]
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 : 125
Date solved : Tuesday, September 30, 2025 at 03:51:15 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \sin \left (x \right )-\cos \left (x \right ) y-3 \sin \left (x \right ) y^{\prime }+3 \left (1+\cos \left (x \right )\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=sin(x)-cos(x)*y(x)-3*sin(x)*diff(y(x),x)+3*(cos(x)+1)*diff(diff(y(x),x),x)+(x+sin(x))*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 28

ode=Sin[x] - Cos[x]*y[x] - 3*Sin[x]*D[y[x],x] + 3*(1 + Cos[x])*D[y[x],{x,2}] + (x + Sin[x])*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

NotImplementedError : The given ODE -(x*Derivative(y(x), (x, 3)) + (Derivative(y(x), (x, 3)) + 1)*si