Internal problem ID [15179]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 13. Basic concepts and definitions. Exercises
page 98
Problem number: 321.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {\left (x -1\right ) y^{\prime \prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve((x-1)*diff(y(x),x$2)=1,y(x), singsol=all)
\[ y = \ln \left (x -1\right ) \left (x -1\right )+\left (c_{1} -1\right ) x +c_{2} +1 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[(x-1)*y''[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (x-1) \log (x-1)+(-1+c_2) x+c_1 \]