Internal problem ID [5322]
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]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x -y+2}{x +y-1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.703 (sec). Leaf size: 35
dsolve(diff(y(x),x)=(x-y(x)+2)/(x+y(x)-1),y(x), singsol=all)
\[ y \relax (x ) = \frac {3}{2}-\frac {\left (2 x +1\right ) c_{1}+\sqrt {2 \left (2 x +1\right )^{2} c_{1}^{2}+1}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 49
DSolve[y'[x]==(x-y[x]+2)/(x+y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {2 x (x+1)+1+c_1}+1 \\ y(x)\to -x+\sqrt {2 x (x+1)+1+c_1}+1 \\ \end{align*}