49.21.13 problem 5(a)

Internal problem ID [7743]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 5(a)
Date solved : Monday, January 27, 2025 at 03:11:46 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x -y+2}{x +y-1} \end{align*}

✓ Solution by Maple

Time used: 0.214 (sec). Leaf size: 33

dsolve(diff(y(x),x)=(x-y(x)+2)/(x+y(x)-1),y(x), singsol=all)
 

\[ y = \frac {-\sqrt {1+8 \left (x +\frac {1}{2}\right )^{2} c_{1}^{2}}+\left (-2 x +2\right ) c_{1}}{2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.162 (sec). Leaf size: 53

DSolve[D[y[x],x]==(x-y[x]+2)/(x+y[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

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