32.10.4 problem Exercise 35.4, page 504

Internal problem ID [5998]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.4, page 504
Date solved : Sunday, March 30, 2025 at 10:29:27 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.186 (sec). Leaf size: 15

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

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