77.26.16 problem 16

Internal problem ID [20625]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 16
Date solved : Thursday, October 02, 2025 at 06:16:23 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

\[ y = \frac {\ln \left (x \right )^{4} x}{24}+\ln \left (x \right )+4+c_1 x +c_2 x \ln \left (x \right )+c_3 x \ln \left (x \right )^{2}+c_4 x \ln \left (x \right )^{3} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 44

ode=x^4*D[y[x],{x,4}]+2*x^3*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==x+Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{24} x \log ^4(x)+\log (x)+c_1 x+c_4 x \log ^3(x)+c_3 x \log ^2(x)+c_2 x \log (x)+4 \end{align*}

✓ Sympy. Time used: 0.256 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = C_{1} x + C_{2} x \log {\left (x \right )} + C_{3} x \log {\left (x \right )}^{2} + C_{4} x \log {\left (x \right )}^{3} + \frac {x \log {\left (x \right )}^{4}}{24} + \log {\left (x \right )} + 4 \]