Internal problem ID [3167]
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`]]
\[ \boxed {y^{2} x -2 y+\left (x^{2} y-2 y-2 x \right ) y^{\prime }=-x -3} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 89
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 \left (x \right ) &= \frac {2 x +\sqrt {-x^{4}-6 x^{3}+\left (-2 c_{1} +6\right ) x^{2}+12 x +4 c_{1}}}{x^{2}-2} \\ y \left (x \right ) &= \frac {2 x -\sqrt {-x^{4}-6 x^{3}+\left (-2 c_{1} +6\right ) x^{2}+12 x +4 c_{1}}}{x^{2}-2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.549 (sec). Leaf size: 95
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^4-6 x^3+(6+c_1) x^2+12 x-2 c_1}}{x^2-2} \\ y(x)\to \frac {2 x+\sqrt {-x^4-6 x^3+(6+c_1) x^2+12 x-2 c_1}}{x^2-2} \\ \end{align*}