Internal problem ID [3177]
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`]]
\[ \boxed {y+\left (3 x^{2} y-x \right ) y^{\prime }=-x^{2}-2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 67
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 \left (x \right ) &= \frac {1-\sqrt {-12 \ln \left (x \right ) x^{2}-6 c_{1} x^{2}-6 x^{3}+1}}{3 x} \\ y \left (x \right ) &= \frac {1+\sqrt {-12 \ln \left (x \right ) x^{2}-6 c_{1} x^{2}-6 x^{3}+1}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.543 (sec). Leaf size: 96
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-\sqrt {\frac {1}{x^2}} x \sqrt {-6 x^3-12 x^2 \log (x)+9 c_1 x^2+1}}{3 x} \\ 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*}