Internal problem ID [4654]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x^2*diff(y(x),x$2)+x*(diff(y(x),x))=1,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} +c_{1} \ln \left (x \right )+\frac {\ln \left (x \right )^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 21
DSolve[x^2*y''[x]+x*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\log ^2(x)}{2}+c_1 \log (x)+c_2 \]