Internal problem ID [4976]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 113
dsolve((x+2*x^3)+(y(x)+2*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2-2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1}-1}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2-2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1}-1}}}{2} \\ y \relax (x ) = -\frac {\sqrt {-2+2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1}-1}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2+2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1}-1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.449 (sec). Leaf size: 147
DSolve[(x+2*x^3)+(y[x]+2*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-1-\sqrt {-4 \left (x^4+x^2\right )+1+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1-\sqrt {-4 \left (x^4+x^2\right )+1+8 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-1+\sqrt {-4 \left (x^4+x^2\right )+1+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1+\sqrt {-4 \left (x^4+x^2\right )+1+8 c_1}}}{\sqrt {2}} \\ \end{align*}