Internal problem ID [5788]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations
problems. page 12
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y-\left (2 x +y-4\right ) y^{\prime }=-2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(y(x)+2=(2*x+y(x)-4)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-4 c_{1} +1+\sqrt {1+4 \left (x -3\right ) c_{1}}}{2 c_{1}} \\ y \left (x \right ) &= \frac {-4 c_{1} +1-\sqrt {1+4 \left (x -3\right ) c_{1}}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 82
DSolve[y[x]+2==(2*x+y[x]-4)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {1+4 c_1 (x-3)}-1+4 c_1}{2 c_1} \\ y(x)\to \frac {\sqrt {1+4 c_1 (x-3)}+1-4 c_1}{2 c_1} \\ y(x)\to -2 \\ y(x)\to \text {Indeterminate} \\ y(x)\to 1-x \\ \end{align*}