75.13.4 problem 321

Internal problem ID [16909]
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 ODEs). Section 13. Basic concepts and definitions. Exercises page 98
Problem number : 321
Date solved : Tuesday, January 28, 2025 at 09:40:36 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.000 (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)*D[y[x],{x,2}]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x-1) \log (x-1)+(-1+c_2) x+c_1 \]