Internal problem ID [7899]
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]`]]
\[ \boxed {\left (x^{2} y^{3}+y x \right ) y^{\prime }-1=0} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = \frac {\sqrt {x \left (2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right ) x +2 x -1\right )}}{x} \\ y \left (x \right ) = -\frac {\sqrt {x \left (2 \operatorname {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: 0.118 (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 W\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {2 x W\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}} \\ \end{align*}