Internal problem ID [2666]
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: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 53
dsolve((4*x*y(x)+3*y(x)^2-x)+x*(x+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-x^{3}+\sqrt {x^{6}+x^{5}-4 c_{1} x}}{2 x^{2}} \\ y \relax (x ) = -\frac {x^{3}+\sqrt {x^{6}+x^{5}-4 c_{1} x}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.404 (sec). Leaf size: 80
DSolve[(4*x*y[x]+3*y[x]^2-x)+x*(x+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^4+\sqrt {x^2} \sqrt {x^6+x^5+4 c_1 x}}{2 x^3} \\ y(x)\to -\frac {x}{2}+\frac {\sqrt {x^2} \sqrt {x^6+x^5+4 c_1 x}}{2 x^3} \\ \end{align*}