81.6.14 problem 14

Internal problem ID [18626]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 14
Date solved : Monday, March 31, 2025 at 05:46:58 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }&=-\frac {1}{x^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=x^2*diff(diff(diff(y(x),x),x),x)+5*x*diff(diff(y(x),x),x)+4*diff(y(x),x) = -1/x^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 40

ode=x^2*D[y[x],{x,3}]+5*x*D[y[x],{x,2}]+4*D[y[x],x]==-1/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\log ^2(x)+2 c_3 x+(2-4 c_2) \log (x)+2-2 c_1-4 c_2}{2 x} \]

✓ Sympy. Time used: 0.321 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 3)) + 5*x*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), x) + x**(-2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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