Internal problem ID [2665]
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: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 73
dsolve(y(x)*(2*x-y(x)+2)+2*(x-y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left ({\mathrm e}^{x} c_{1} x +\sqrt {{\mathrm e}^{2 x} c_{1}^{2} x^{2}+c_{1} {\mathrm e}^{x}}\right ) {\mathrm e}^{-x}}{c_{1}} \\ y \relax (x ) = -\frac {\left (-{\mathrm e}^{x} c_{1} x +\sqrt {{\mathrm e}^{2 x} c_{1}^{2} x^{2}+c_{1} {\mathrm e}^{x}}\right ) {\mathrm e}^{-x}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 43.085 (sec). Leaf size: 125
DSolve[y[x]*(2*x-y[x]+2)+2*(x-y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-e^{-x} \sqrt {e^x \left (e^x x^2-e^{2 c_1}\right )} \\ y(x)\to x+e^{-x} \sqrt {e^x \left (e^x x^2-e^{2 c_1}\right )} \\ y(x)\to x-e^{-x} \sqrt {e^{2 x} x^2} \\ y(x)\to e^{-x} \sqrt {e^{2 x} x^2}+x \\ \end{align*}