Internal problem ID [1055]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve((3*x^2+2*y(x))+(2*y(x)+2*x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x -\sqrt {-x^{3}+x^{2}-c_{1}} \\ y \relax (x ) = -x +\sqrt {-x^{3}+x^{2}-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 49
DSolve[(3*x^2+2*y[x])+(2*y[x]+2*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {-x^3+x^2+c_1} \\ y(x)\to -x+\sqrt {-x^3+x^2+c_1} \\ \end{align*}