23.5.65 problem 65

Internal problem ID [6674]
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 : 65
Date solved : Tuesday, September 30, 2025 at 03:50:45 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \sin \left (x \right ) y-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 40

ode:=sin(x)*y(x)-2*cos(x)*diff(y(x),x)-sin(x)*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 +\frac {\int \left (8 c_1 x +4 c_2 -3 x^{2}+2 x^{2} \ln \left (x \right )\right ) {\mathrm e}^{\cos \left (x \right )}d x}{4}\right ) {\mathrm e}^{-\cos \left (x \right )} \]

✓ Mathematica. Time used: 0.989 (sec). Leaf size: 57

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

\begin{align*} y(x)&\to e^{-\cos (x)} \left (\int _1^x\frac {1}{4} e^{\cos (K[1])} \left (2 \log (K[1]) K[1]^2-3 K[1]^2+4 c_1 K[1]+4 c_2\right )dK[1]+c_3\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -(y(x)*sin(x) - log(x) - sin(x)*Derivative(y(x), (x, 2)) + Deriv