Internal problem ID [2653]
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]]
Solve \begin {gather*} \boxed {y+2-\left (2 x +y-4\right ) y^{\prime }=0} \end {gather*}
✓ 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 \relax (x ) = \frac {1-4 c_{1}+\sqrt {4 c_{1} x -12 c_{1}+1}}{2 c_{1}} \\ y \relax (x ) = -\frac {-1+4 c_{1}+\sqrt {4 c_{1} x -12 c_{1}+1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.261 (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*}