Internal problem ID [3982]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise
10.15, page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 50
dsolve((y(x)^2+12*x^2*y(x))+(2*x*y(x)+4*x^3)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2 x^{3}+\sqrt {4 x^{6}+c_{1} x}}{x} \\ y \relax (x ) = -\frac {2 x^{3}+\sqrt {4 x^{6}+c_{1} x}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.639 (sec). Leaf size: 58
DSolve[(y[x]^2+12*x^2*y[x])+(2*x*y[x]+4*x^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x} \\ y(x)\to \frac {-2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x} \\ \end{align*}