Internal problem ID [2658]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x y^{2}+x -2 y+3+\left (y x^{2}-2 y-2 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 92
dsolve((x*y(x)^2+x-2*y(x)+3)+(x^2*y(x)-2*(x+y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {2 x +\sqrt {-x^{4}-2 c_{1} x^{2}-6 x^{3}+6 x^{2}+4 c_{1}+12 x}}{x^{2}-2} \\ y \relax (x ) = -\frac {-2 x +\sqrt {-x^{4}-2 c_{1} x^{2}-6 x^{3}+6 x^{2}+4 c_{1}+12 x}}{x^{2}-2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.352 (sec). Leaf size: 85
DSolve[(x*y[x]^2+x-2*y[x]+3)+(x^2*y[x]-2*(x+y[x]))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x-\sqrt {x (12+x (-x (x+6)+6+c_1))-2 c_1}}{x^2-2} \\ y(x)\to \frac {2 x+\sqrt {x (12+x (-x (x+6)+6+c_1))-2 c_1}}{x^2-2} \\ \end{align*}