Internal problem ID [7889]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 309.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 113
dsolve((2*y(x)^3+y(x))*diff(y(x),x)-2*x^3-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: 2.771 (sec). Leaf size: 143
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 {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1-\sqrt {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-1+\sqrt {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-1+\sqrt {\left (2 x^2+1\right )^2+8 c_1}}}{\sqrt {2}} \\ \end{align*}