Internal problem ID [13248]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }=\frac {x +1}{x -1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)=(x+1)/(x-1),y(x), singsol=all)
\[ y \left (x \right ) = 2+2 \ln \left (-1+x \right ) \left (-1+x \right )+\frac {x^{2}}{2}+\left (c_{1} -2\right ) x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 30
DSolve[y''[x]==(x+1)/(x-1),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{2}+2 (x-1) \log (x-1)+(-2+c_2) x+c_1 \]