Internal problem ID [7880]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 300.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {6 y^{\prime } y^{2} x +2 y^{3}+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 120
dsolve(6*x*y(x)^2*diff(y(x),x)+2*y(x)^3+x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (\left (-2 x^{2}+8 c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x} \\ y \relax (x ) = -\frac {\left (\left (-2 x^{2}+8 c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}-\frac {i \sqrt {3}\, \left (\left (-2 x^{2}+8 c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{4 x} \\ y \relax (x ) = -\frac {\left (\left (-2 x^{2}+8 c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}+\frac {i \sqrt {3}\, \left (\left (-2 x^{2}+8 c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.383 (sec). Leaf size: 99
DSolve[6*x*y[x]^2*y'[x]+2*y[x]^3+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ \end{align*}