Internal problem ID [4051]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.38, page 103.
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 {\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+12 y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.065 (sec). Leaf size: 50
dsolve((2*x*y(x)+4*x^3)*diff(y(x),x)+y(x)^2+12*x^2*y(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: 0.258 (sec). Leaf size: 58
DSolve[(2*x*y[x]+4*x^3)*y'[x]+y[x]^2+12*x^2*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*}