Internal problem ID [4146]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x^2*diff(y(x),x$2)+x*(diff(y(x),x))=1,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \relax (x )^{2}}{2}+c_{1} \ln \relax (x )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 21
DSolve[x^2*y''[x]+x*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log ^2(x)}{2}+c_1 \log (x)+c_2 \\ \end{align*}