Internal problem ID [2657]
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: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve((2*x^2-x*y(x)^2-2*y(x)+3)-(x^2*y(x)+2*x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2-\frac {\sqrt {12 x^{3}+54 x +18 c_{1}+36}}{3}}{x} \\ y \relax (x ) = \frac {-2+\frac {\sqrt {12 x^{3}+54 x +18 c_{1}+36}}{3}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.613 (sec). Leaf size: 87
DSolve[(2*x^2-x*y[x]^2-2*y[x]+3)-(x^2*y[x]+2*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {6 x+\sqrt {3} \sqrt {x^2 \left (4 x^3+18 x+12+3 c_1\right )}}{3 x^2} \\ y(x)\to \frac {-6 x+\sqrt {3} \sqrt {x^2 \left (4 x^3+18 x+12+3 c_1\right )}}{3 x^2} \\ \end{align*}