82.48.3 problem Ex. 3

Internal problem ID [18913]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 3
Date solved : Monday, March 31, 2025 at 06:24:25 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y&=0 \end{align*}

✗ Maple

ode:=(x^3+x+1)*diff(diff(diff(y(x),x),x),x)+(3+6*x)*diff(diff(y(x),x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(1+x+x^3)*D[y[x],{x,3}]+(3+6*x)*D[y[x],{x,2}]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((6*x + 3)*Derivative(y(x), (x, 2)) + (x**3 + x + 1)*Derivative(y(x), (x, 3)) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve (6*x + 3)*Derivative(y(x), (x, 2)) + (x**3 + x + 1)*Derivative(y(x), (x, 3)) + 6*y(x)