83.27.15 problem 15

Internal problem ID [19290]
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. Exercise VII (A) at page 104
Problem number : 15
Date solved : Monday, March 31, 2025 at 07:05:48 PM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y&=\ln \left (x \right ) \end{align*}

✗ Maple

ode:=x^5*diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+x^4*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+x*diff(y(x),x)+y(x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^5*D[y[x],{x,6}]+x^4*D[y[x],{x,5}]+x*D[y[x],x]+y[x]==Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*Derivative(y(x), (x, 6)) + x**4*Derivative(y(x), (x, 5)) + x*Derivative(y(x), x) + y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**4*(x*Derivative(y(x), (x, 6)) + Derivative(y(x), (x, 5))) - y(x) + log(x))/x cannot be solved by the factorable group method