83.48.1 problem Ex 1 page 96

Internal problem ID [19522]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 1 page 96
Date solved : Monday, March 31, 2025 at 07:29:09 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=(x^2+x+1)*diff(diff(diff(y(x),x),x),x)+(3+6*x)*diff(diff(y(x),x),x)+6*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}+c_2 x +c_3}{x^{2}+x +1} \]

✓ Mathematica. Time used: 0.263 (sec). Leaf size: 42

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

\[ y(x)\to \frac {c_1 \left (8 x-4 i \sqrt {3}+4\right )-c_2}{4 \left (x^2+x+1\right )}+c_3 \]

✗ Sympy

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

NotImplementedError : The given ODE x**2*Derivative(y(x), (x, 3))/6 + x*Derivative(y(x), (x, 2)) + x*Derivative(y(x), (x, 3))/6 + Derivative(y(x), x) + Derivative(y(x), (x, 2))/2 + Derivative(y(x), (x, 3))/6 cannot be solved by the factorable group method