Internal problem ID [3162]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 17.
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: 0.015 (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 {1-4 c_{1} +\sqrt {4 c_{1} x -12 c_{1} +1}}{2 c_{1}} y \left (x \right ) = -\frac {-1+4 c_{1} +\sqrt {4 c_{1} x -12 c_{1} +1}}{2 c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.28 (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*}