81.1.11 problem 10

Internal problem ID [18527]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 10
Date solved : Thursday, March 13, 2025 at 12:11:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 18

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

\[ y \left (x \right ) = c_{2} x^{5}+c_{1} x +\frac {1}{12 x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

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

\[ y(x)\to c_2 x^5+\frac {1}{12 x}+c_1 x \]

✓ Sympy. Time used: 0.351 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 5*y(x) - 1/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + C_{2} x^{5} + \frac {1}{12 x} \]