73.1.25 problem 2.4 (c)

Internal problem ID [15003]
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 : Tuesday, January 28, 2025 at 07:27:21 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*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 13

dsolve([diff(y(x),x)=(x-1)/(x+1),y(0) = 8],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 25

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

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