Internal problem ID [8645]
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]
\[ \boxed {\left (2 y^{3}+y\right ) y^{\prime }=2 x^{3}+x} \]
✓ Solution by Maple
Time used: 0.015 (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 \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: 2.343 (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*}