67.1.25 problem 2.4 (c)

Internal problem ID [16290]
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 : 2.4 (c)
Date solved : Thursday, October 02, 2025 at 10:45:24 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 13

ode:=diff(y(x),x) = (x-1)/(1+x); 
ic:=[y(0) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x -2 \ln \left (x +1\right )+8 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 25

ode=D[y[x],x]==(x-1)/(x+1); 
ic={y[0]==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _0^x\frac {K[1]-1}{K[1]+1}dK[1]+8 \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - x)/(x + 1) + Derivative(y(x), x),0) 
ics = {y(0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x - 2 \log {\left (x + 1 \right )} + 8 \]