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 : Monday, January 27, 2025 at 01:30:41 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

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

dsolve(x^2*diff(y(x),x$2)+x*(diff(y(x),x))=1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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