Internal problem ID [5729]
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]
\[ \boxed {\left (2 y^{3}+y\right ) y^{\prime }=-2 x^{3}-x} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) &= -\frac {\sqrt {-2-2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1} -1}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-2-2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1} -1}}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {-2+2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1} -1}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-2+2 \sqrt {-4 x^{4}-4 x^{2}-8 c_{1} -1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.086 (sec). Leaf size: 151
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 x^4-4 x^2+1+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1-\sqrt {-4 x^4-4 x^2+1+8 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-1+\sqrt {-4 x^4-4 x^2+1+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1+\sqrt {-4 x^4-4 x^2+1+8 c_1}}}{\sqrt {2}} \\ \end{align*}