Internal problem ID [4031]
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 12.18, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+8 y^{3} x^{3}+2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(diff(y(x),x)+8*x^3*y(x)^3+2*x*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {{\mathrm e}^{2 x^{2}} c_{1}-4 x^{2}-2}} \\ y \relax (x ) = -\frac {1}{\sqrt {{\mathrm e}^{2 x^{2}} c_{1}-4 x^{2}-2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.32 (sec). Leaf size: 58
DSolve[y'[x]+8*x^3*y[x]^3+2*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {-4 x^2+c_1 e^{2 x^2}-2}} \\ y(x)\to \frac {1}{\sqrt {-4 x^2+c_1 e^{2 x^2}-2}} \\ y(x)\to 0 \\ \end{align*}