73.1.6 problem 2.2 (f)

Internal problem ID [14984]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (f)
Date solved : Tuesday, January 28, 2025 at 07:26:36 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)=(x+1)/(x-1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]==(x+1)/(x-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[2]}\frac {K[1]+1}{K[1]-1}dK[1]dK[2]+c_2 x+c_1 \]