Internal problem ID [10806]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 57.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x +y-3}{1-x +y}=0} \]
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 32
dsolve(diff(y(x),x)= (x+y(x)-3)/(1-x+y(x)),y(x), singsol=all)
\[ y \left (x \right ) = 1-\frac {-\left (x -2\right ) c_{1} +\sqrt {2 \left (x -2\right )^{2} c_{1}^{2}+1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 55
DSolve[y'[x]== (x+y[x]-3)/(1-x+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-i \sqrt {-2 (x-4) x-1-c_1}-1 \\ y(x)\to x+i \sqrt {-2 (x-4) x-1-c_1}-1 \\ \end{align*}