Internal problem ID [7896]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 316.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 53
dsolve((2*x*y(x)^3+y(x))*diff(y(x),x)+2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {-2 \RootOf \left ({\mathrm e}^{\textit {\_Z}} \expIntegral \left (1, \textit {\_Z}\right )+4 c_{1} {\mathrm e}^{\textit {\_Z}}-4 x \right )} \\ y \relax (x ) = -\sqrt {-2 \RootOf \left ({\mathrm e}^{\textit {\_Z}} \expIntegral \left (1, \textit {\_Z}\right )+4 c_{1} {\mathrm e}^{\textit {\_Z}}-4 x \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.525 (sec). Leaf size: 53
DSolve[2*y[x]^2 + (y[x] + 2*x*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ \text {Solve}\left [x=-\frac {1}{4} e^{-\frac {1}{2} y(x)^2} \text {Ei}\left (\frac {y(x)^2}{2}\right )+c_1 e^{-\frac {1}{2} y(x)^2},y(x)\right ] \\ y(x)\to 0 \\ \end{align*}