15.16.9 problem 9

Internal problem ID [3229]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:21:59 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {1}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

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

\[ y = \frac {4 x^{2} c_2 \ln \left (x \right )+4 c_3 \,x^{2}+\ln \left (x \right )+c_1 +1}{4 x} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 33

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

\[ y(x)\to \frac {\log (x)+1}{4 x}+\frac {c_1}{x}+c_2 x+c_3 x \log (x) \]

✓ Sympy. Time used: 0.328 (sec). Leaf size: 22

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

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