25.1.27 problem 27

Internal problem ID [4239]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 27
Date solved : Monday, January 27, 2025 at 08:43:36 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +y-1\right ) y^{\prime }&=x -y+1 \end{align*}

✓ Solution by Maple

Time used: 0.536 (sec). Leaf size: 28

dsolve((x+y(x)-1)*diff(y(x),x)=(x-y(x)+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 47

DSolve[(x+y[x]-1)*D[y[x],x]==(x-y[x]+1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {2 x^2+1+c_1}-x+1 \\ y(x)\to \sqrt {2 x^2+1+c_1}-x+1 \\ \end{align*}