73.1.6 problem 2.2 (f)

Internal problem ID [14905]
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 : Thursday, March 13, 2025 at 05:20:34 AM
CAS classification : [[_2nd_order, _quadrature]]

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

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

ode:=diff(diff(y(x),x),x) = (1+x)/(x-1); 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.206 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - (x + 1)/(x - 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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