Internal problem ID [8652]
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]`]]
\[ \boxed {\left (2 y^{3} x +y\right ) y^{\prime }+2 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 60
dsolve((2*x*y(x)^3+y(x))*diff(y(x),x)+2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sqrt {2}\, \sqrt {-\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \operatorname {expIntegral}_{1}\left (\textit {\_Z} \right )+4 c_{1} {\mathrm e}^{\textit {\_Z}}-4 x \right )} \\ y \left (x \right ) &= -\sqrt {2}\, \sqrt {-\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \operatorname {expIntegral}_{1}\left (\textit {\_Z} \right )+4 c_{1} {\mathrm e}^{\textit {\_Z}}-4 x \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.319 (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} \operatorname {ExpIntegralEi}\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*}