Internal problem ID [2668]
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: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x^{2}+2 x +y+\left (3 y x^{2}-x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 65
dsolve((x^2+2*x+y(x))+(3*x^2*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-1+\sqrt {-12 \ln \relax (x ) x^{2}-6 c_{1} x^{2}-6 x^{3}+1}}{3 x} \\ y \relax (x ) = \frac {1+\sqrt {-12 \ln \relax (x ) x^{2}-6 c_{1} x^{2}-6 x^{3}+1}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 94
DSolve[(x^2+2*x+y[x])+(3*x^2*y[x]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (\frac {1}{x}-\sqrt {\frac {1}{x^2}} \sqrt {-6 x^3-12 x^2 \log (x)+9 c_1 x^2+1}\right ) \\ y(x)\to \frac {1+\sqrt {\frac {1}{x^2}} x \sqrt {-6 x^3-12 x^2 \log (x)+9 c_1 x^2+1}}{3 x} \\ \end{align*}