Internal problem ID [6075]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x -y+2}{y+x -1}=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 35
dsolve(diff(y(x),x)=(x-y(x)+2)/(x+y(x)-1),y(x), singsol=all)
\[ y \left (x \right ) = \frac {3}{2}-\frac {\left (2 x +1\right ) c_{1} +\sqrt {2 \left (2 x +1\right )^{2} c_{1}^{2}+1}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.154 (sec). Leaf size: 53
DSolve[y'[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*}