32.10.20 problem Exercise 35.20, page 504

Internal problem ID [6014]
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 35.20, page 504
Date solved : Monday, January 27, 2025 at 01:32:32 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{2} \left (\log ^2(x)+4 \log (x)+2\right ) \]