Internal problem ID [7900]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 320.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (x^{2} y^{3}+x y\right ) y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 70
dsolve((x^2*y(x)^3+x*y(x))*diff(y(x),x)-1 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {x \left (2 \LambertW \left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right ) x +2 x -1\right )}}{x} \\ y \relax (x ) = -\frac {\sqrt {x \left (2 \LambertW \left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right ) x +2 x -1\right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 76
DSolve[-1 + (x*y[x] + x^2*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2 x \text {ProductLog}\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {2 x \text {ProductLog}\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}} \\ \end{align*}