77.35.14 problem 14

Internal problem ID [20718]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Misc. Exercise on chapter VII. Page 118
Problem number : 14
Date solved : Thursday, October 02, 2025 at 06:22:22 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y&=6 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 44

ode:=(x^3-4*x)*diff(diff(diff(y(x),x),x),x)+(9*x^2-4)*diff(diff(y(x),x),x)+18*x*diff(y(x),x)+6*y(x) = 6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {8 \ln \left (x \right ) c_1 x +x^{4}-c_1 \,x^{3}+\left (c_2 -12\right ) x^{2}+c_3 x +4 c_2}{\left (x +2\right )^{2} \left (x -2\right )^{2}} \]

✓ Mathematica. Time used: 0.148 (sec). Leaf size: 83

ode=(x^3-4*x)*D[y[x],{x,3}]+(9*x^2-4)*D[y[x],{x,2}]+18*x*D[y[x],x]+6*y[x]==6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {6 x^4-3 c_3 x^3+2 (-24+c_1-c_2+3 c_3) x^2-2 (2 c_1-5 c_2+18 c_3) x+24 c_3 x \log (x)+8 (12+c_1-c_2+3 c_3)}{6 \left (x^2-4\right )^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(18*x*Derivative(y(x), x) + (9*x**2 - 4)*Derivative(y(x), (x, 2)) + (x**3 - 4*x)*Derivative(y(x), (x, 3)) + 6*y(x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x*(-x**2*Derivative(y(x), (x, 3)) - 9*x*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3))) - 6*y(x) + 4*Derivative(y(x), (x, 2)) + 6)/(18*x) cannot be solved by the factorable group method