Internal problem ID [3175]
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`]]
\[ \boxed {4 y x +3 y^{2}+x \left (x +2 y\right ) y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
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 \left (x \right ) &= \frac {-x^{3}+\sqrt {x \left (x^{5}+x^{4}-4 c_{1} \right )}}{2 x^{2}} \\ y \left (x \right ) &= \frac {-x^{3}-\sqrt {x \left (x^{5}+x^{4}-4 c_{1} \right )}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.621 (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*}